integrate constants

simplifyAssertEq(Constant(1):integrate(x), x)
${\int{{1}}d x} = {x}$
GOOD
time: 0.372000ms
stack: size: 7
  • Init
  • Prune
  • Expand
  • Prune
  • Factor
  • Prune
  • Tidy

simplifyAssertEq(y:integrate(x), x * y)
${\int{{y}}d x} = {{{x}} {{y}}}$
GOOD
time: 1.064000ms
stack: size: 8
  • Init
  • Prune
  • Expand
  • Prune
  • Factor
  • Prune
  • *:Tidy:apply
  • Tidy


simplifyAssertEq(Constant(1):integrate(x, xL, xR), (xR - xL))
${\int\limits_{{xL}}^{{xR}}{{1}}d x} = {{xR}{-{xL}}}$
GOOD
time: 3.149000ms
stack: size: 12
  • Init
  • unm:Prune:doubleNegative
  • Prune
  • Expand
  • Prune
  • +:Factor:apply
  • Factor
  • Prune
  • Constant:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • Tidy

definite integral bounds:
simplifyAssertEq(x:integrate(x, xL, xR), ((xR^2 - xL^2)/2)) -- hmm, the infamous minus sign factoring simplificaiton error...
instead I'll just test this ...
simplifyAssertEq((x:integrate(x, xL, xR) - (xR^2 - xL^2)/2), Constant(0))
${{\int\limits_{{xL}}^{{xR}}{{x}}d x}{-{{\frac{1}{2}}{\left({{{xR}^{2}}{-{{xL}^{2}}}}\right)}}}} = {0}$
GOOD
time: 11.416000ms
stack: size: 73
  • Init
  • Integral:Prune:apply
  • Integral:Prune:apply
  • unm:Prune:doubleNegative
  • *:Prune:factorDenominators
  • unm:Prune:doubleNegative
  • *:Prune:apply
  • *:Prune:factorDenominators
  • *:Prune:apply
  • *:Prune:factorDenominators
  • *:Prune:factorDenominators
  • unm:Prune:doubleNegative
  • *:Prune:flatten
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • ^:Prune:xToTheZero
  • /:Prune:divToPowSub
  • *:Prune:factorDenominators
  • +:Prune:factorOutDivs
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • ^:Prune:xToTheZero
  • Constant:Tidy:apply
  • Constant:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • Constant:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • unm:Prune:doubleNegative
  • unm:Prune:doubleNegative
  • unm:Prune:doubleNegative
  • *:Prune:apply
  • /:Prune:divToPowSub
  • *:Prune:factorDenominators
  • +:Prune:flatten
  • +:Prune:factorOutDivs
  • +:Prune:flatten
  • Prune
  • ^:Expand:integerPower
  • ^:Expand:integerPower
  • *:Expand:apply
  • ^:Expand:integerPower
  • ^:Expand:integerPower
  • Expand
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • *:Prune:apply
  • *:Prune:flatten
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • *:Prune:apply
  • *:Prune:apply
  • +:Prune:flattenAddMul
  • +:Prune:combineConstants
  • +:Prune:flattenAddMul
  • +:Prune:flatten
  • /:Prune:zeroOverX
  • Prune
  • Factor
  • Prune
  • Expand
  • Prune
  • Factor
  • Prune
  • Constant:Tidy:apply
  • Tidy

$x^n$ integrals:

simplifyAssertEq(x:integrate(x), x^2 / 2)
${\int{{x}}d x} = {{\frac{1}{2}} {{x}^{2}}}$
GOOD
time: 4.845000ms
stack: size: 17
  • Init
  • Prune
  • ^:Expand:integerPower
  • Expand
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • Prune
  • /:Factor:polydiv
  • Factor
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • ^:Prune:xToTheZero
  • *:Prune:apply
  • /:Prune:divToPowSub
  • *:Prune:factorDenominators
  • Prune
  • Tidy

simplifyAssertEq((x^2):integrate(x), x^3 / 3)
${\int{{{x}^{2}}}d x} = {{\frac{1}{3}} {{x}^{3}}}$
GOOD
time: 4.880000ms
stack: size: 17
  • Init
  • Prune
  • ^:Expand:integerPower
  • Expand
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • Prune
  • /:Factor:polydiv
  • Factor
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • ^:Prune:xToTheZero
  • *:Prune:apply
  • /:Prune:divToPowSub
  • *:Prune:factorDenominators
  • Prune
  • Tidy

simplifyAssertEq(((x^-2):integrate(x) - (-1/x)), Constant(0))
${{\int{{{x}^{-2}}}d x}{-{\frac{-1}{x}}}} = {0}$
GOOD
time: 3.827000ms
stack: size: 8
  • Init
  • ^:Prune:xToTheNegY
  • Prune
  • Expand
  • Prune
  • Factor
  • Prune
  • Tidy

simplifyAssertEq((1/x):integrate(x), log(abs(x)))
${\int{{\frac{1}{x}}}d x} = {\log\left( {\left| x\right|}\right)}$
GOOD
time: 2.405000ms
stack: size: 7
  • Init
  • Prune
  • Expand
  • Prune
  • Factor
  • Prune
  • Tidy

simplifyAssertEq((x^-1):integrate(x), log(abs(x)))
${\int{{{x}^{-1}}}d x} = {\log\left( {\left| x\right|}\right)}$
GOOD
time: 0.999000ms
stack: size: 7
  • Init
  • Prune
  • Expand
  • Prune
  • Factor
  • Prune
  • Tidy

simplifyAssertEq((1/(2*x^2)):integrate(x), -(1/(2*x)))
${\int{{\frac{1}{{{2}} {{{x}^{2}}}}}}d x} = {-{\frac{1}{{{2}} {{x}}}}}$
GOOD
time: 6.057000ms
stack: size: 16
  • Init
  • *:Prune:apply
  • *:Prune:factorDenominators
  • unm:Prune:doubleNegative
  • Prune
  • Expand
  • Prune
  • /:Factor:polydiv
  • Factor
  • /:Prune:xOverMinusOne
  • *:Prune:flatten
  • Prune
  • Constant:Tidy:apply
  • *:Tidy:apply
  • /:Tidy:apply
  • Tidy


simplifyAssertEq((x^frac(1,2)):integrate(x), frac(2 * x * sqrt(x), 3))
${\int{{{x}^{\frac{1}{2}}}}d x} = {{\frac{1}{3}} {{{2}} {{x}} {{\sqrt{x}}}}}$
GOOD
time: 5.638000ms
stack: size: 20
  • Init
  • sqrt:Prune:apply
  • +:Prune:combineConstants
  • +:Prune:factorOutDivs
  • *:Prune:combinePows
  • Prune
  • Expand
  • Prune
  • /:Factor:polydiv
  • Factor
  • *:Prune:flatten
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • ^:Prune:xToTheZero
  • /:Prune:divToPowSub
  • *:Prune:factorDenominators
  • Prune
  • ^:Tidy:replacePowerOfFractionWithRoots
  • *:Tidy:apply
  • Tidy

simplifyAssertEq(sqrt(x):integrate(x), frac(2 * x * sqrt(x), 3))
${\int{{\sqrt{x}}}d x} = {{\frac{1}{3}} {{{2}} {{x}} {{\sqrt{x}}}}}$
GOOD
time: 5.369000ms
stack: size: 20
  • Init
  • sqrt:Prune:apply
  • +:Prune:combineConstants
  • +:Prune:factorOutDivs
  • *:Prune:combinePows
  • Prune
  • Expand
  • Prune
  • /:Factor:polydiv
  • Factor
  • *:Prune:flatten
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • ^:Prune:xToTheZero
  • /:Prune:divToPowSub
  • *:Prune:factorDenominators
  • Prune
  • ^:Tidy:replacePowerOfFractionWithRoots
  • *:Tidy:apply
  • Tidy


simplifyAssertEq((1/x):integrate(x), log(abs(x)))
${\int{{\frac{1}{x}}}d x} = {\log\left( {\left| x\right|}\right)}$
GOOD
time: 0.908000ms
stack: size: 7
  • Init
  • Prune
  • Expand
  • Prune
  • Factor
  • Prune
  • Tidy


simplifyAssertEq((2/x):integrate(x), (2*log(abs(x))))
${\int{{\frac{2}{x}}}d x} = {{{2}} {{\log\left( {\left| x\right|}\right)}}}$
GOOD
time: 1.822000ms
stack: size: 12
  • Init
  • *:Prune:logPow
  • Prune
  • ^:Expand:integerPower
  • log:Expand:apply
  • Expand
  • *:Prune:logPow
  • +:Prune:flattenAddMul
  • Prune
  • Factor
  • Prune
  • Tidy

simplifyAssertEq((1/(2*x)):integrate(x), (log(abs(x))/2))
${\int{{\frac{1}{{{2}} {{x}}}}}d x} = {{\frac{1}{2}} {\log\left( {\left| x\right|}\right)}}$
GOOD
time: 3.453000ms
stack: size: 13
  • Init
  • /:Prune:logPow
  • Prune
  • log:Expand:apply
  • Expand
  • *:Prune:apply
  • /:Prune:logPow
  • *:Prune:factorDenominators
  • Prune
  • Factor
  • Prune
  • ^:Tidy:replacePowerOfFractionWithRoots
  • Tidy


simplifyAssertEq((1/(x*(3*x+4))):integrate(x)(), log(1 / abs( (4 + 3 * x) / x)^frac(1,4)))
${\log\left( {{\left({\frac{1}{\left|{{\frac{1}{x}}{\left({{4} + {{{3}} {{x}}}}\right)}}\right|}}\right)}^{\frac{1}{4}}}\right)} = {\log\left( {\frac{1}{{\left|{{\frac{1}{x}}{\left({{4} + {{{3}} {{x}}}}\right)}}\right|}^{\frac{1}{4}}}}\right)}$
GOOD
time: 28.305000ms
stack: size: 20
  • Init
  • Prune
  • log:Expand:apply
  • unm:Expand:apply
  • log:Expand:apply
  • Expand
  • log:Prune:apply
  • ^:Prune:xToTheNegY
  • *:Prune:logPow
  • /:Prune:logPow
  • *:Prune:factorDenominators
  • +:Prune:combineConstants
  • Prune
  • Factor
  • Prune
  • Expand
  • Prune
  • Factor
  • Prune
  • Tidy


simplifyAssertEq(f:diff(x):integrate(x)(), f)
${f} = {f}$
GOOD
time: 0.268000ms
stack: size: 7
  • Init
  • Prune
  • Expand
  • Prune
  • Factor
  • Prune
  • Tidy

simplifyAssertEq(f:integrate(x):diff(x)(), f)
${f} = {f}$
GOOD
time: 0.360000ms
stack: size: 8
  • Init
  • Derivative:Prune:integrals
  • Prune
  • Expand
  • Prune
  • Factor
  • Prune
  • Tidy

simplifyAssertEq(f:diff(x,x):integrate(x)(), f:diff(x))
${\frac{\partial f}{\partial x}} = {\frac{\partial f}{\partial x}}$
GOOD
time: 0.535000ms
stack: size: 7
  • Init
  • Prune
  • Expand
  • Prune
  • Factor
  • Prune
  • Tidy

simplifyAssertEq(f:integrate(x):integrate(x):diff(x)(), f:integrate(x))
${\int{{f}}d x} = {\int{{f}}d x}$
GOOD
time: 0.721000ms
stack: size: 7
  • Init
  • Prune
  • Expand
  • Prune
  • Factor
  • Prune
  • Tidy

simplifyAssertEq(f:integrate(x):diff(x,x)(), f:diff(x))
${\frac{\partial f}{\partial x}} = {\frac{\partial f}{\partial x}}$
GOOD
time: 0.342000ms
stack: size: 7
  • Init
  • Prune
  • Expand
  • Prune
  • Factor
  • Prune
  • Tidy


simplifyAssertEq(sin(x):integrate(x)(), -cos(x))
${-{\cos\left( x\right)}} = {-{\cos\left( x\right)}}$
GOOD
time: 0.892000ms
stack: size: 11
  • Init
  • unm:Prune:doubleNegative
  • Prune
  • Expand
  • Prune
  • Factor
  • Prune
  • Constant:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • Tidy

simplifyAssertEq(cos(x):integrate(x)(), sin(x))
${\sin\left( x\right)} = {\sin\left( x\right)}$
GOOD
time: 0.489000ms
stack: size: 7
  • Init
  • Prune
  • Expand
  • Prune
  • Factor
  • Prune
  • Tidy


simplifyAssertEq(sin(2*x):integrate(x)(), (-cos(2*x)/2))
${-{{\frac{1}{2}} {\cos\left( {{{2}} {{x}}}\right)}}} = {{\frac{1}{2}}{\left({-{\cos\left( {{{2}} {{x}}}\right)}}\right)}}$
GOOD
time: 4.131000ms
stack: size: 22
  • Init
  • unm:Prune:doubleNegative
  • Prune
  • Expand
  • Prune
  • /:Factor:polydiv
  • Factor
  • *:Prune:flatten
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • ^:Prune:xToTheZero
  • /:Prune:divToPowSub
  • *:Prune:factorDenominators
  • Prune
  • Constant:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • /:Tidy:apply
  • Tidy

simplifyAssertEq(cos(y*x):integrate(x)(), (sin(y*x)/y))
${{\frac{1}{y}} {\sin\left( {{{x}} {{y}}}\right)}} = {{\frac{1}{y}} {\sin\left( {{{y}} {{x}}}\right)}}$
GOOD
time: 3.823000ms
stack: size: 15
  • Init
  • Prune
  • Expand
  • Prune
  • /:Factor:polydiv
  • Factor
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • ^:Prune:xToTheZero
  • *:Prune:apply
  • /:Prune:divToPowSub
  • *:Prune:factorDenominators
  • Prune
  • *:Tidy:apply
  • Tidy


simplifyAssertEq((cos(x)/sin(x)):integrate(x), log(abs(sin(x))))
${\int{{\frac{\cos\left( x\right)}{\sin\left( x\right)}}}d x} = {\log\left( {\left|{\sin\left( x\right)}\right|}\right)}$
GOOD
time: 4.045000ms
stack: size: 7
  • Init
  • Prune
  • Expand
  • Prune
  • Factor
  • Prune
  • Tidy


simplifyAssertEq((cos(x)^2):integrate(x)(), frac(1,4) * (2 * x + sin(2 * x)))
${{\frac{1}{4}}{\left({{\sin\left( {{{2}} {{x}}}\right)} + {{{2}} {{x}}}}\right)}} = {{{\frac{1}{4}}} {{\left({{{{2}} {{x}}} + {\sin\left( {{{2}} {{x}}}\right)}}\right)}}}$
GOOD
time: 6.017000ms
stack: size: 30
  • Init
  • *:Tidy:apply
  • *:Tidy:apply
  • *:Prune:apply
  • *:Prune:factorDenominators
  • Prune
  • Expand
  • Prune
  • +:Factor:apply
  • /:Factor:polydiv
  • Factor
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • ^:Prune:xToTheNegY
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • ^:Prune:xToTheZero
  • *:Tidy:apply
  • *:Tidy:apply
  • *:Prune:apply
  • /:Prune:divToPowSub
  • *:Prune:factorDenominators
  • /:Prune:divToPowSub
  • *:Prune:factorDenominators
  • Prune
  • *:Tidy:apply
  • *:Tidy:apply
  • Tidy


simplifyAssertEq(sinh(x):integrate(x), cosh(x))
${\int{{\sinh\left( x\right)}}d x} = {\cosh\left( x\right)}$
GOOD
time: 0.538000ms
stack: size: 7
  • Init
  • Prune
  • Expand
  • Prune
  • Factor
  • Prune
  • Tidy

simplifyAssertEq(cosh(x):integrate(x), sinh(x))
${\int{{\cosh\left( x\right)}}d x} = {\sinh\left( x\right)}$
GOOD
time: 0.671000ms
stack: size: 7
  • Init
  • Prune
  • Expand
  • Prune
  • Factor
  • Prune
  • Tidy


multiple integrals


simplifyAssertEq((x * y):integrate(x), frac(1,2) * x^2 * y)
${\int{{\left({{{x}} {{y}}}\right)}}d x} = {{{\frac{1}{2}}} {{{x}^{2}}} {{y}}}$
GOOD
time: 2.893000ms
stack: size: 19
  • Init
  • *:Prune:factorDenominators
  • Prune
  • ^:Expand:integerPower
  • Expand
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • Prune
  • /:Factor:polydiv
  • Factor
  • *:Prune:flatten
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • ^:Prune:xToTheZero
  • /:Prune:divToPowSub
  • *:Prune:factorDenominators
  • Prune
  • *:Tidy:apply
  • Tidy

simplifyAssertEq((x * y):integrate(x)():integrate(y)(), frac(1,4) * x^2 * y^2)
${{\frac{1}{4}} {{{{x}^{2}}} {{{y}^{2}}}}} = {{{\frac{1}{4}}} {{{x}^{2}}} {{{y}^{2}}}}$
GOOD
time: 7.469000ms
stack: size: 31
  • Init
  • *:Prune:factorDenominators
  • Prune
  • ^:Expand:integerPower
  • ^:Expand:integerPower
  • Expand
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • Prune
  • *:Factor:combineMulOfLikePow
  • /:Factor:polydiv
  • Factor
  • ^:Prune:expandMulOfLikePow
  • *:Prune:flatten
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • ^:Prune:xToTheNegY
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • ^:Prune:xToTheZero
  • /:Prune:divToPowSub
  • *:Prune:factorDenominators
  • /:Prune:divToPowSub
  • *:Prune:factorDenominators
  • Prune
  • *:Tidy:apply
  • Tidy

simplifyAssertEq((x * y):integrate(x):integrate(y)(), frac(1,4) * x^2 * y^2)
${{\frac{1}{4}} {{{{x}^{2}}} {{{y}^{2}}}}} = {{{\frac{1}{4}}} {{{x}^{2}}} {{{y}^{2}}}}$
GOOD
time: 6.860000ms
stack: size: 31
  • Init
  • *:Prune:factorDenominators
  • Prune
  • ^:Expand:integerPower
  • ^:Expand:integerPower
  • Expand
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • Prune
  • *:Factor:combineMulOfLikePow
  • /:Factor:polydiv
  • Factor
  • ^:Prune:expandMulOfLikePow
  • *:Prune:flatten
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • ^:Prune:xToTheNegY
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • ^:Prune:xToTheZero
  • /:Prune:divToPowSub
  • *:Prune:factorDenominators
  • /:Prune:divToPowSub
  • *:Prune:factorDenominators
  • Prune
  • *:Tidy:apply
  • Tidy

simplifyAssertEq((r * cos(x)):integrate(r)():integrate(x)(), frac(1,2) * r^2 * sin(x))
${{\frac{1}{2}} {{{{r}^{2}}} {{\sin\left( x\right)}}}} = {{{\frac{1}{2}}} {{{r}^{2}}} {{\sin\left( x\right)}}}$
GOOD
time: 7.775000ms
stack: size: 19
  • Init
  • *:Prune:factorDenominators
  • Prune
  • ^:Expand:integerPower
  • Expand
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • Prune
  • /:Factor:polydiv
  • Factor
  • *:Prune:flatten
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • ^:Prune:xToTheZero
  • /:Prune:divToPowSub
  • *:Prune:factorDenominators
  • Prune
  • *:Tidy:apply
  • Tidy

simplifyAssertEq((r * cos(x)):integrate(x)():integrate(r)(), frac(1,2) * r^2 * sin(x))
${{\frac{1}{2}} {{{{r}^{2}}} {{\sin\left( x\right)}}}} = {{{\frac{1}{2}}} {{{r}^{2}}} {{\sin\left( x\right)}}}$
GOOD
time: 7.570000ms
stack: size: 19
  • Init
  • *:Prune:factorDenominators
  • Prune
  • ^:Expand:integerPower
  • Expand
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • Prune
  • /:Factor:polydiv
  • Factor
  • *:Prune:flatten
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • ^:Prune:xToTheZero
  • /:Prune:divToPowSub
  • *:Prune:factorDenominators
  • Prune
  • *:Tidy:apply
  • Tidy


simplifyAssertEq( ( cosh(a * x) * sinh(a * x) ):integrate(x), cosh(a * x)^2 / (2 * a) )
${\int{{\left({{{\cosh\left( {{{a}} {{x}}}\right)}} {{\sinh\left( {{{a}} {{x}}}\right)}}}\right)}}d x} = {\frac{{\cosh\left( {{{a}} {{x}}}\right)}^{2}}{{{2}} {{a}}}}$
GOOD
time: 6.377000ms
stack: size: 26
  • Init
  • Prune
  • ^:Expand:integerPower
  • Expand
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • Prune
  • ^:ExpandPolynomial:apply
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • ^:ExpandPolynomial:apply
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • /:Factor:polydiv
  • Factor
  • *:Prune:flatten
  • *:Prune:apply
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • ^:Prune:xToTheZero
  • /:Prune:divToPowSub
  • *:Prune:factorDenominators
  • Prune
  • *:Tidy:apply
  • *:Tidy:apply
  • Tidy

simplifyAssertEq( ( cosh(a * x) * sinh(b * x) ):integrate(x), 1 / ((a + b) * (a - b)) * (-b * cosh(a*x) * cosh(b*x) + a * sinh(a*x) * sinh(b*x)) )
${\int{{\left({{{\cosh\left( {{{a}} {{x}}}\right)}} {{\sinh\left( {{{b}} {{x}}}\right)}}}\right)}}d x} = {{{\frac{1}{{{\left({{a} + {b}}\right)}} {{\left({{a}{-{b}}}\right)}}}}} {{\left({{ {-{b}} {{\cosh\left( {{{a}} {{x}}}\right)}} {{\cosh\left( {{{b}} {{x}}}\right)}}} + {{{a}} {{\sinh\left( {{{a}} {{x}}}\right)}} {{\sinh\left( {{{b}} {{x}}}\right)}}}}\right)}}}$
GOOD
time: 76.903000ms
stack: size: 78
  • Init
  • unm:Prune:doubleNegative
  • unm:Prune:doubleNegative
  • *:Prune:flatten
  • Constant:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • *:Tidy:apply
  • unm:Prune:doubleNegative
  • *:Prune:apply
  • *:Prune:factorDenominators
  • Prune
  • *:Expand:apply
  • *:Expand:apply
  • *:Expand:apply
  • Expand
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • *:Prune:flatten
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • *:Prune:flatten
  • *:Prune:apply
  • +:Prune:combineConstants
  • +:Prune:flattenAddMul
  • +:Prune:flatten
  • Prune
  • +:Factor:apply
  • /:Prune:xOverX
  • ^:Prune:xToTheOne
  • /:Prune:xOverX
  • ^:Prune:xToTheOne
  • /:Prune:xOverX
  • ^:Prune:xToTheOne
  • /:Prune:xOverX
  • ^:Prune:xToTheOne
  • unm:Prune:doubleNegative
  • +:Factor:apply
  • +:Factor:apply
  • +:Factor:apply
  • *:ExpandPolynomial:apply
  • *:ExpandPolynomial:apply
  • *:ExpandPolynomial:apply
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • *:Prune:flatten
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • *:Prune:flatten
  • *:Prune:apply
  • +:Prune:combineConstants
  • +:Prune:flattenAddMul
  • +:Prune:flatten
  • *:ExpandPolynomial:apply
  • *:ExpandPolynomial:apply
  • *:ExpandPolynomial:apply
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • *:Prune:flatten
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • *:Prune:flatten
  • *:Prune:apply
  • +:Prune:combineConstants
  • +:Prune:flattenAddMul
  • +:Prune:flatten
  • Factor
  • Prune
  • Tidy


simplifyAssertEq( ( sinh(a * x)^2 * cosh(a * x) ):integrate(x), sinh(a * x)^3 / (3 * a) )
${\int{{\left({{{{\sinh\left( {{{a}} {{x}}}\right)}^{2}}} {{\cosh\left( {{{a}} {{x}}}\right)}}}\right)}}d x} = {\frac{{\sinh\left( {{{a}} {{x}}}\right)}^{3}}{{{3}} {{a}}}}$
GOOD
time: 4.013000ms
stack: size: 26
  • Init
  • Prune
  • ^:Expand:integerPower
  • Expand
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • Prune
  • ^:ExpandPolynomial:apply
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • ^:ExpandPolynomial:apply
  • +:Prune:combineConstants
  • *:Prune:combinePows
  • /:Factor:polydiv
  • Factor
  • *:Prune:flatten
  • *:Prune:apply
  • unm:Prune:doubleNegative
  • +:Prune:combineConstants
  • ^:Prune:xToTheZero
  • /:Prune:divToPowSub
  • *:Prune:factorDenominators
  • Prune
  • *:Tidy:apply
  • *:Tidy:apply
  • Tidy