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