3.90.37 \(\int \frac {-36 x^4-162 e^4 x^4+81 x^4 \log (3)+e^{4 x} (-162 e^4+81 \log (3))+e^{3 x} (648 e^4 x-324 x \log (3))+e^{2 x} (-108 x^2-972 e^4 x^2+54 x^3+18 x^4+486 x^2 \log (3))+e^x (144 x^3+648 e^4 x^3-54 x^4-18 x^5-324 x^3 \log (3))}{324 e^8 x^4-36 e^4 x^5+x^6+(-324 e^4 x^4+18 x^5) \log (3)+81 x^4 \log ^2(3)+e^{4 x} (324 e^8-324 e^4 \log (3)+81 \log ^2(3))+e^{3 x} (-1296 e^8 x+1296 e^4 x \log (3)-324 x \log ^2(3))+e^{2 x} (1944 e^8 x^2-36 e^4 x^3+(-1944 e^4 x^2+18 x^3) \log (3)+486 x^2 \log ^2(3))+e^x (-1296 e^8 x^3+72 e^4 x^4+(1296 e^4 x^3-36 x^4) \log (3)-324 x^3 \log ^2(3))} \, dx\)

Optimal. Leaf size=28 \[ \frac {4+x}{-2 e^4+\frac {x}{\left (3-\frac {3 e^x}{x}\right )^2}+\log (3)} \]

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Rubi [F]  time = 41.10, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-36 x^4-162 e^4 x^4+81 x^4 \log (3)+e^{4 x} \left (-162 e^4+81 \log (3)\right )+e^{3 x} \left (648 e^4 x-324 x \log (3)\right )+e^{2 x} \left (-108 x^2-972 e^4 x^2+54 x^3+18 x^4+486 x^2 \log (3)\right )+e^x \left (144 x^3+648 e^4 x^3-54 x^4-18 x^5-324 x^3 \log (3)\right )}{324 e^8 x^4-36 e^4 x^5+x^6+\left (-324 e^4 x^4+18 x^5\right ) \log (3)+81 x^4 \log ^2(3)+e^{4 x} \left (324 e^8-324 e^4 \log (3)+81 \log ^2(3)\right )+e^{3 x} \left (-1296 e^8 x+1296 e^4 x \log (3)-324 x \log ^2(3)\right )+e^{2 x} \left (1944 e^8 x^2-36 e^4 x^3+\left (-1944 e^4 x^2+18 x^3\right ) \log (3)+486 x^2 \log ^2(3)\right )+e^x \left (-1296 e^8 x^3+72 e^4 x^4+\left (1296 e^4 x^3-36 x^4\right ) \log (3)-324 x^3 \log ^2(3)\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-36*x^4 - 162*E^4*x^4 + 81*x^4*Log[3] + E^(4*x)*(-162*E^4 + 81*Log[3]) + E^(3*x)*(648*E^4*x - 324*x*Log[3
]) + E^(2*x)*(-108*x^2 - 972*E^4*x^2 + 54*x^3 + 18*x^4 + 486*x^2*Log[3]) + E^x*(144*x^3 + 648*E^4*x^3 - 54*x^4
- 18*x^5 - 324*x^3*Log[3]))/(324*E^8*x^4 - 36*E^4*x^5 + x^6 + (-324*E^4*x^4 + 18*x^5)*Log[3] + 81*x^4*Log[3]^
2 + E^(4*x)*(324*E^8 - 324*E^4*Log[3] + 81*Log[3]^2) + E^(3*x)*(-1296*E^8*x + 1296*E^4*x*Log[3] - 324*x*Log[3]
^2) + E^(2*x)*(1944*E^8*x^2 - 36*E^4*x^3 + (-1944*E^4*x^2 + 18*x^3)*Log[3] + 486*x^2*Log[3]^2) + E^x*(-1296*E^
8*x^3 + 72*E^4*x^4 + (1296*E^4*x^3 - 36*x^4)*Log[3] - 324*x^3*Log[3]^2)),x]

[Out]

-(x/(2*E^4 - Log[3])) - 72*Defer[Int][(E^x*x^3)/(x^3 - 18*E^(4 + 2*x)*(1 - Log[3]/(2*E^4)) + 36*E^(4 + x)*x*(1
- Log[3]/(2*E^4)) - 18*E^4*x^2*(1 - Log[3]/(2*E^4)))^2, x] + 72*Defer[Int][x^4/(x^3 - 18*E^(4 + 2*x)*(1 - Log
[3]/(2*E^4)) + 36*E^(4 + x)*x*(1 - Log[3]/(2*E^4)) - 18*E^4*x^2*(1 - Log[3]/(2*E^4)))^2, x] + 54*Defer[Int][(E
^x*x^4)/(x^3 - 18*E^(4 + 2*x)*(1 - Log[3]/(2*E^4)) + 36*E^(4 + x)*x*(1 - Log[3]/(2*E^4)) - 18*E^4*x^2*(1 - Log
[3]/(2*E^4)))^2, x] + 18*Defer[Int][x^5/(x^3 - 18*E^(4 + 2*x)*(1 - Log[3]/(2*E^4)) + 36*E^(4 + x)*x*(1 - Log[3
]/(2*E^4)) - 18*E^4*x^2*(1 - Log[3]/(2*E^4)))^2, x] - (12*(1 + 12*E^4 - Log[729])*Defer[Int][x^5/(x^3 - 18*E^(
4 + 2*x)*(1 - Log[3]/(2*E^4)) + 36*E^(4 + x)*x*(1 - Log[3]/(2*E^4)) - 18*E^4*x^2*(1 - Log[3]/(2*E^4)))^2, x])/
(2*E^4 - Log[3]) + 18*Defer[Int][(E^x*x^5)/(x^3 - 18*E^(4 + 2*x)*(1 - Log[3]/(2*E^4)) + 36*E^(4 + x)*x*(1 - Lo
g[3]/(2*E^4)) - 18*E^4*x^2*(1 - Log[3]/(2*E^4)))^2, x] + (8*Defer[Int][x^6/(x^3 - 18*E^(4 + 2*x)*(1 - Log[3]/(
2*E^4)) + 36*E^(4 + x)*x*(1 - Log[3]/(2*E^4)) - 18*E^4*x^2*(1 - Log[3]/(2*E^4)))^2, x])/(2*E^4 - Log[3]) - (3*
(1 + 12*E^4 - Log[729])*Defer[Int][x^6/(x^3 - 18*E^(4 + 2*x)*(1 - Log[3]/(2*E^4)) + 36*E^(4 + x)*x*(1 - Log[3]
/(2*E^4)) - 18*E^4*x^2*(1 - Log[3]/(2*E^4)))^2, x])/(2*E^4 - Log[3]) + (2*Defer[Int][x^7/(x^3 - 18*E^(4 + 2*x)
*(1 - Log[3]/(2*E^4)) + 36*E^(4 + x)*x*(1 - Log[3]/(2*E^4)) - 18*E^4*x^2*(1 - Log[3]/(2*E^4)))^2, x])/(2*E^4 -
Log[3]) + (12*Defer[Int][x^2/(x^3 - 18*E^(4 + 2*x)*(1 - Log[3]/(2*E^4)) + 36*E^(4 + x)*x*(1 - Log[3]/(2*E^4))
- 18*E^4*x^2*(1 - Log[3]/(2*E^4))), x])/(2*E^4 - Log[3]) + (4*Defer[Int][x^3/(-x^3 + 18*E^(4 + 2*x)*(1 - Log[
3]/(2*E^4)) - 36*E^(4 + x)*x*(1 - Log[3]/(2*E^4)) + 18*E^4*x^2*(1 - Log[3]/(2*E^4))), x])/(2*E^4 - Log[3]) + (
2*Defer[Int][x^4/(-x^3 + 18*E^(4 + 2*x)*(1 - Log[3]/(2*E^4)) - 36*E^(4 + x)*x*(1 - Log[3]/(2*E^4)) + 18*E^4*x^
2*(1 - Log[3]/(2*E^4))), x])/(2*E^4 - Log[3])

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (-36-162 e^4\right ) x^4+81 x^4 \log (3)+e^{4 x} \left (-162 e^4+81 \log (3)\right )+e^{3 x} \left (648 e^4 x-324 x \log (3)\right )+e^{2 x} \left (-108 x^2-972 e^4 x^2+54 x^3+18 x^4+486 x^2 \log (3)\right )+e^x \left (144 x^3+648 e^4 x^3-54 x^4-18 x^5-324 x^3 \log (3)\right )}{324 e^8 x^4-36 e^4 x^5+x^6+\left (-324 e^4 x^4+18 x^5\right ) \log (3)+81 x^4 \log ^2(3)+e^{4 x} \left (324 e^8-324 e^4 \log (3)+81 \log ^2(3)\right )+e^{3 x} \left (-1296 e^8 x+1296 e^4 x \log (3)-324 x \log ^2(3)\right )+e^{2 x} \left (1944 e^8 x^2-36 e^4 x^3+\left (-1944 e^4 x^2+18 x^3\right ) \log (3)+486 x^2 \log ^2(3)\right )+e^x \left (-1296 e^8 x^3+72 e^4 x^4+\left (1296 e^4 x^3-36 x^4\right ) \log (3)-324 x^3 \log ^2(3)\right )} \, dx\\ &=\int \frac {x^4 \left (-36-162 e^4+81 \log (3)\right )+e^{4 x} \left (-162 e^4+81 \log (3)\right )+e^{3 x} \left (648 e^4 x-324 x \log (3)\right )+e^{2 x} \left (-108 x^2-972 e^4 x^2+54 x^3+18 x^4+486 x^2 \log (3)\right )+e^x \left (144 x^3+648 e^4 x^3-54 x^4-18 x^5-324 x^3 \log (3)\right )}{324 e^8 x^4-36 e^4 x^5+x^6+\left (-324 e^4 x^4+18 x^5\right ) \log (3)+81 x^4 \log ^2(3)+e^{4 x} \left (324 e^8-324 e^4 \log (3)+81 \log ^2(3)\right )+e^{3 x} \left (-1296 e^8 x+1296 e^4 x \log (3)-324 x \log ^2(3)\right )+e^{2 x} \left (1944 e^8 x^2-36 e^4 x^3+\left (-1944 e^4 x^2+18 x^3\right ) \log (3)+486 x^2 \log ^2(3)\right )+e^x \left (-1296 e^8 x^3+72 e^4 x^4+\left (1296 e^4 x^3-36 x^4\right ) \log (3)-324 x^3 \log ^2(3)\right )} \, dx\\ &=\int \frac {x^4 \left (-36-162 e^4+81 \log (3)\right )+e^{4 x} \left (-162 e^4+81 \log (3)\right )+e^{3 x} \left (648 e^4 x-324 x \log (3)\right )+e^{2 x} \left (-108 x^2-972 e^4 x^2+54 x^3+18 x^4+486 x^2 \log (3)\right )+e^x \left (144 x^3+648 e^4 x^3-54 x^4-18 x^5-324 x^3 \log (3)\right )}{-36 e^4 x^5+x^6+\left (-324 e^4 x^4+18 x^5\right ) \log (3)+x^4 \left (324 e^8+81 \log ^2(3)\right )+e^{4 x} \left (324 e^8-324 e^4 \log (3)+81 \log ^2(3)\right )+e^{3 x} \left (-1296 e^8 x+1296 e^4 x \log (3)-324 x \log ^2(3)\right )+e^{2 x} \left (1944 e^8 x^2-36 e^4 x^3+\left (-1944 e^4 x^2+18 x^3\right ) \log (3)+486 x^2 \log ^2(3)\right )+e^x \left (-1296 e^8 x^3+72 e^4 x^4+\left (1296 e^4 x^3-36 x^4\right ) \log (3)-324 x^3 \log ^2(3)\right )} \, dx\\ &=\int \frac {9 \left (e^x-x\right ) \left (-54 e^{4+x} x^2+18 e^4 x^3 \left (1+\frac {4-9 \log (3)}{18 e^4}\right )+e^x x^2 \left (-12+6 x+2 x^2+27 \log (3)\right )-18 e^{4+3 x} \left (1-\frac {\log (3)}{2 e^4}\right )+54 e^{4+2 x} x \left (1-\frac {\log (3)}{2 e^4}\right )\right )}{\left (18 e^4 x^2-x^2 (x+9 \log (3))+18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )-36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2} \, dx\\ &=9 \int \frac {\left (e^x-x\right ) \left (-54 e^{4+x} x^2+18 e^4 x^3 \left (1+\frac {4-9 \log (3)}{18 e^4}\right )+e^x x^2 \left (-12+6 x+2 x^2+27 \log (3)\right )-18 e^{4+3 x} \left (1-\frac {\log (3)}{2 e^4}\right )+54 e^{4+2 x} x \left (1-\frac {\log (3)}{2 e^4}\right )\right )}{\left (18 e^4 x^2-x^2 (x+9 \log (3))+18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )-36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2} \, dx\\ &=9 \int \left (-\frac {1}{9 \left (2 e^4-\log (3)\right )}+\frac {2 x^2 \left (6-2 x-x^2\right )}{9 \left (2 e^4-\log (3)\right ) \left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )}+\frac {x^3 (4+x) \left (2 x^3-36 e^{4+x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^4 x \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-3 x^2 \left (1+12 e^4-\log (729)\right )\right )}{9 \left (2 e^4-\log (3)\right ) \left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2}\right ) \, dx\\ &=-\frac {x}{2 e^4-\log (3)}+\frac {\int \frac {x^3 (4+x) \left (2 x^3-36 e^{4+x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^4 x \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-3 x^2 \left (1+12 e^4-\log (729)\right )\right )}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2} \, dx}{2 e^4-\log (3)}+\frac {2 \int \frac {x^2 \left (6-2 x-x^2\right )}{x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )} \, dx}{2 e^4-\log (3)}\\ &=-\frac {x}{2 e^4-\log (3)}+\frac {\int \left (\frac {4 x^3 \left (2 x^3-36 e^{4+x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^4 x \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-3 x^2 \left (1+12 e^4-\log (729)\right )\right )}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2}+\frac {x^4 \left (2 x^3-36 e^{4+x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^4 x \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-3 x^2 \left (1+12 e^4-\log (729)\right )\right )}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2}\right ) \, dx}{2 e^4-\log (3)}+\frac {2 \int \left (\frac {6 x^2}{x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )}+\frac {2 x^3}{-x^3+18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )-36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )+18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )}+\frac {x^4}{-x^3+18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )-36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )+18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )}\right ) \, dx}{2 e^4-\log (3)}\\ &=-\frac {x}{2 e^4-\log (3)}+\frac {\int \frac {x^4 \left (2 x^3-36 e^{4+x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^4 x \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-3 x^2 \left (1+12 e^4-\log (729)\right )\right )}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2} \, dx}{2 e^4-\log (3)}+\frac {2 \int \frac {x^4}{-x^3+18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )-36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )+18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )} \, dx}{2 e^4-\log (3)}+\frac {4 \int \frac {x^3}{-x^3+18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )-36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )+18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )} \, dx}{2 e^4-\log (3)}+\frac {4 \int \frac {x^3 \left (2 x^3-36 e^{4+x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^4 x \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-3 x^2 \left (1+12 e^4-\log (729)\right )\right )}{\left (x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )\right )^2} \, dx}{2 e^4-\log (3)}+\frac {12 \int \frac {x^2}{x^3-18 e^{4+2 x} \left (1-\frac {\log (3)}{2 e^4}\right )+36 e^{4+x} x \left (1-\frac {\log (3)}{2 e^4}\right )-18 e^4 x^2 \left (1-\frac {\log (3)}{2 e^4}\right )} \, dx}{2 e^4-\log (3)}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.25, size = 79, normalized size = 2.82 \begin {gather*} -\frac {x-\frac {x^3 (4+x)}{-18 e^{4+2 x}+36 e^{4+x} x-18 e^4 x^2+9 e^{2 x} \log (3)-18 e^x x \log (3)+x^2 (x+9 \log (3))}}{2 e^4-\log (3)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-36*x^4 - 162*E^4*x^4 + 81*x^4*Log[3] + E^(4*x)*(-162*E^4 + 81*Log[3]) + E^(3*x)*(648*E^4*x - 324*x
*Log[3]) + E^(2*x)*(-108*x^2 - 972*E^4*x^2 + 54*x^3 + 18*x^4 + 486*x^2*Log[3]) + E^x*(144*x^3 + 648*E^4*x^3 -
54*x^4 - 18*x^5 - 324*x^3*Log[3]))/(324*E^8*x^4 - 36*E^4*x^5 + x^6 + (-324*E^4*x^4 + 18*x^5)*Log[3] + 81*x^4*L
og[3]^2 + E^(4*x)*(324*E^8 - 324*E^4*Log[3] + 81*Log[3]^2) + E^(3*x)*(-1296*E^8*x + 1296*E^4*x*Log[3] - 324*x*
Log[3]^2) + E^(2*x)*(1944*E^8*x^2 - 36*E^4*x^3 + (-1944*E^4*x^2 + 18*x^3)*Log[3] + 486*x^2*Log[3]^2) + E^x*(-1
296*E^8*x^3 + 72*E^4*x^4 + (1296*E^4*x^3 - 36*x^4)*Log[3] - 324*x^3*Log[3]^2)),x]

[Out]

-((x - (x^3*(4 + x))/(-18*E^(4 + 2*x) + 36*E^(4 + x)*x - 18*E^4*x^2 + 9*E^(2*x)*Log[3] - 18*E^x*x*Log[3] + x^2
*(x + 9*Log[3])))/(2*E^4 - Log[3]))

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fricas [B]  time = 0.52, size = 145, normalized size = 5.18 \begin {gather*} \frac {18 \, x^{3} e^{4} - 9 \, x^{3} \log \relax (3) + 4 \, x^{3} + 9 \, {\left (2 \, x e^{4} - x \log \relax (3)\right )} e^{\left (2 \, x\right )} - 18 \, {\left (2 \, x^{2} e^{4} - x^{2} \log \relax (3)\right )} e^{x}}{2 \, x^{3} e^{4} - 9 \, x^{2} \log \relax (3)^{2} - 36 \, x^{2} e^{8} + 9 \, {\left (4 \, e^{4} \log \relax (3) - \log \relax (3)^{2} - 4 \, e^{8}\right )} e^{\left (2 \, x\right )} - 18 \, {\left (4 \, x e^{4} \log \relax (3) - x \log \relax (3)^{2} - 4 \, x e^{8}\right )} e^{x} - {\left (x^{3} - 36 \, x^{2} e^{4}\right )} \log \relax (3)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((81*log(3)-162*exp(4))*exp(x)^4+(-324*x*log(3)+648*x*exp(4))*exp(x)^3+(486*x^2*log(3)-972*x^2*exp(4
)+18*x^4+54*x^3-108*x^2)*exp(x)^2+(-324*x^3*log(3)+648*x^3*exp(4)-18*x^5-54*x^4+144*x^3)*exp(x)+81*x^4*log(3)-
162*x^4*exp(4)-36*x^4)/((81*log(3)^2-324*exp(4)*log(3)+324*exp(4)^2)*exp(x)^4+(-324*x*log(3)^2+1296*exp(4)*x*l
og(3)-1296*x*exp(4)^2)*exp(x)^3+(486*x^2*log(3)^2+(-1944*x^2*exp(4)+18*x^3)*log(3)+1944*x^2*exp(4)^2-36*x^3*ex
p(4))*exp(x)^2+(-324*x^3*log(3)^2+(1296*x^3*exp(4)-36*x^4)*log(3)-1296*x^3*exp(4)^2+72*x^4*exp(4))*exp(x)+81*x
^4*log(3)^2+(-324*x^4*exp(4)+18*x^5)*log(3)+324*x^4*exp(4)^2-36*x^5*exp(4)+x^6),x, algorithm="fricas")

[Out]

(18*x^3*e^4 - 9*x^3*log(3) + 4*x^3 + 9*(2*x*e^4 - x*log(3))*e^(2*x) - 18*(2*x^2*e^4 - x^2*log(3))*e^x)/(2*x^3*
e^4 - 9*x^2*log(3)^2 - 36*x^2*e^8 + 9*(4*e^4*log(3) - log(3)^2 - 4*e^8)*e^(2*x) - 18*(4*x*e^4*log(3) - x*log(3
)^2 - 4*x*e^8)*e^x - (x^3 - 36*x^2*e^4)*log(3))

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((81*log(3)-162*exp(4))*exp(x)^4+(-324*x*log(3)+648*x*exp(4))*exp(x)^3+(486*x^2*log(3)-972*x^2*exp(4
)+18*x^4+54*x^3-108*x^2)*exp(x)^2+(-324*x^3*log(3)+648*x^3*exp(4)-18*x^5-54*x^4+144*x^3)*exp(x)+81*x^4*log(3)-
162*x^4*exp(4)-36*x^4)/((81*log(3)^2-324*exp(4)*log(3)+324*exp(4)^2)*exp(x)^4+(-324*x*log(3)^2+1296*exp(4)*x*l
og(3)-1296*x*exp(4)^2)*exp(x)^3+(486*x^2*log(3)^2+(-1944*x^2*exp(4)+18*x^3)*log(3)+1944*x^2*exp(4)^2-36*x^3*ex
p(4))*exp(x)^2+(-324*x^3*log(3)^2+(1296*x^3*exp(4)-36*x^4)*log(3)-1296*x^3*exp(4)^2+72*x^4*exp(4))*exp(x)+81*x
^4*log(3)^2+(-324*x^4*exp(4)+18*x^5)*log(3)+324*x^4*exp(4)^2-36*x^5*exp(4)+x^6),x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 0.11, size = 87, normalized size = 3.11

method	result	size
risch	\(-\frac {x}{-\ln \relax (3)+2 \,{\mathrm e}^{4}}-\frac {\left (4+x \right ) x^{3}}{\left (-\ln \relax (3)+2 \,{\mathrm e}^{4}\right ) \left (18 \,{\mathrm e}^{2 x +4}-36 x \,{\mathrm e}^{4+x}+18 x^{2} {\mathrm e}^{4}-9 \ln \relax (3) {\mathrm e}^{2 x}+18 x \ln \relax (3) {\mathrm e}^{x}-9 x^{2} \ln \relax (3)-x^{3}\right )}\)	\(87\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((81*ln(3)-162*exp(4))*exp(x)^4+(-324*x*ln(3)+648*x*exp(4))*exp(x)^3+(486*x^2*ln(3)-972*x^2*exp(4)+18*x^4+
54*x^3-108*x^2)*exp(x)^2+(-324*x^3*ln(3)+648*x^3*exp(4)-18*x^5-54*x^4+144*x^3)*exp(x)+81*x^4*ln(3)-162*x^4*exp
(4)-36*x^4)/((81*ln(3)^2-324*exp(4)*ln(3)+324*exp(4)^2)*exp(x)^4+(-324*x*ln(3)^2+1296*exp(4)*x*ln(3)-1296*x*ex
p(4)^2)*exp(x)^3+(486*x^2*ln(3)^2+(-1944*x^2*exp(4)+18*x^3)*ln(3)+1944*x^2*exp(4)^2-36*x^3*exp(4))*exp(x)^2+(-
324*x^3*ln(3)^2+(1296*x^3*exp(4)-36*x^4)*ln(3)-1296*x^3*exp(4)^2+72*x^4*exp(4))*exp(x)+81*x^4*ln(3)^2+(-324*x^
4*exp(4)+18*x^5)*ln(3)+324*x^4*exp(4)^2-36*x^5*exp(4)+x^6),x,method=_RETURNVERBOSE)

[Out]

-x/(-ln(3)+2*exp(4))-(4+x)*x^3/(-ln(3)+2*exp(4))/(18*exp(2*x+4)-36*x*exp(4+x)+18*x^2*exp(4)-9*ln(3)*exp(2*x)+1
8*x*ln(3)*exp(x)-9*x^2*ln(3)-x^3)

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maxima [B]  time = 0.95, size = 131, normalized size = 4.68 \begin {gather*} \frac {x^{3} {\left (18 \, e^{4} - 9 \, \log \relax (3) + 4\right )} - 18 \, x^{2} {\left (2 \, e^{4} - \log \relax (3)\right )} e^{x} + 9 \, x {\left (2 \, e^{4} - \log \relax (3)\right )} e^{\left (2 \, x\right )}}{x^{3} {\left (2 \, e^{4} - \log \relax (3)\right )} + 9 \, {\left (4 \, e^{4} \log \relax (3) - \log \relax (3)^{2} - 4 \, e^{8}\right )} x^{2} - 18 \, {\left (4 \, e^{4} \log \relax (3) - \log \relax (3)^{2} - 4 \, e^{8}\right )} x e^{x} + 9 \, {\left (4 \, e^{4} \log \relax (3) - \log \relax (3)^{2} - 4 \, e^{8}\right )} e^{\left (2 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((81*log(3)-162*exp(4))*exp(x)^4+(-324*x*log(3)+648*x*exp(4))*exp(x)^3+(486*x^2*log(3)-972*x^2*exp(4
)+18*x^4+54*x^3-108*x^2)*exp(x)^2+(-324*x^3*log(3)+648*x^3*exp(4)-18*x^5-54*x^4+144*x^3)*exp(x)+81*x^4*log(3)-
162*x^4*exp(4)-36*x^4)/((81*log(3)^2-324*exp(4)*log(3)+324*exp(4)^2)*exp(x)^4+(-324*x*log(3)^2+1296*exp(4)*x*l
og(3)-1296*x*exp(4)^2)*exp(x)^3+(486*x^2*log(3)^2+(-1944*x^2*exp(4)+18*x^3)*log(3)+1944*x^2*exp(4)^2-36*x^3*ex
p(4))*exp(x)^2+(-324*x^3*log(3)^2+(1296*x^3*exp(4)-36*x^4)*log(3)-1296*x^3*exp(4)^2+72*x^4*exp(4))*exp(x)+81*x
^4*log(3)^2+(-324*x^4*exp(4)+18*x^5)*log(3)+324*x^4*exp(4)^2-36*x^5*exp(4)+x^6),x, algorithm="maxima")

[Out]

(x^3*(18*e^4 - 9*log(3) + 4) - 18*x^2*(2*e^4 - log(3))*e^x + 9*x*(2*e^4 - log(3))*e^(2*x))/(x^3*(2*e^4 - log(3
)) + 9*(4*e^4*log(3) - log(3)^2 - 4*e^8)*x^2 - 18*(4*e^4*log(3) - log(3)^2 - 4*e^8)*x*e^x + 9*(4*e^4*log(3) -
log(3)^2 - 4*e^8)*e^(2*x))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {{\mathrm {e}}^x\,\left (324\,x^3\,\ln \relax (3)-648\,x^3\,{\mathrm {e}}^4-144\,x^3+54\,x^4+18\,x^5\right )-{\mathrm {e}}^{3\,x}\,\left (648\,x\,{\mathrm {e}}^4-324\,x\,\ln \relax (3)\right )+{\mathrm {e}}^{4\,x}\,\left (162\,{\mathrm {e}}^4-81\,\ln \relax (3)\right )+162\,x^4\,{\mathrm {e}}^4-81\,x^4\,\ln \relax (3)+36\,x^4-{\mathrm {e}}^{2\,x}\,\left (486\,x^2\,\ln \relax (3)-972\,x^2\,{\mathrm {e}}^4-108\,x^2+54\,x^3+18\,x^4\right )}{81\,x^4\,{\ln \relax (3)}^2+{\mathrm {e}}^{4\,x}\,\left (324\,{\mathrm {e}}^8-324\,{\mathrm {e}}^4\,\ln \relax (3)+81\,{\ln \relax (3)}^2\right )+{\mathrm {e}}^{2\,x}\,\left (486\,x^2\,{\ln \relax (3)}^2-36\,x^3\,{\mathrm {e}}^4+1944\,x^2\,{\mathrm {e}}^8-\ln \relax (3)\,\left (1944\,x^2\,{\mathrm {e}}^4-18\,x^3\right )\right )-{\mathrm {e}}^{3\,x}\,\left (1296\,x\,{\mathrm {e}}^8+324\,x\,{\ln \relax (3)}^2-1296\,x\,{\mathrm {e}}^4\,\ln \relax (3)\right )-36\,x^5\,{\mathrm {e}}^4+324\,x^4\,{\mathrm {e}}^8-{\mathrm {e}}^x\,\left (324\,x^3\,{\ln \relax (3)}^2-72\,x^4\,{\mathrm {e}}^4+1296\,x^3\,{\mathrm {e}}^8-\ln \relax (3)\,\left (1296\,x^3\,{\mathrm {e}}^4-36\,x^4\right )\right )+x^6-\ln \relax (3)\,\left (324\,x^4\,{\mathrm {e}}^4-18\,x^5\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(x)*(324*x^3*log(3) - 648*x^3*exp(4) - 144*x^3 + 54*x^4 + 18*x^5) - exp(3*x)*(648*x*exp(4) - 324*x*lo
g(3)) + exp(4*x)*(162*exp(4) - 81*log(3)) + 162*x^4*exp(4) - 81*x^4*log(3) + 36*x^4 - exp(2*x)*(486*x^2*log(3)
- 972*x^2*exp(4) - 108*x^2 + 54*x^3 + 18*x^4))/(81*x^4*log(3)^2 + exp(4*x)*(324*exp(8) - 324*exp(4)*log(3) +
81*log(3)^2) + exp(2*x)*(486*x^2*log(3)^2 - 36*x^3*exp(4) + 1944*x^2*exp(8) - log(3)*(1944*x^2*exp(4) - 18*x^3
)) - exp(3*x)*(1296*x*exp(8) + 324*x*log(3)^2 - 1296*x*exp(4)*log(3)) - 36*x^5*exp(4) + 324*x^4*exp(8) - exp(x
)*(324*x^3*log(3)^2 - 72*x^4*exp(4) + 1296*x^3*exp(8) - log(3)*(1296*x^3*exp(4) - 36*x^4)) + x^6 - log(3)*(324
*x^4*exp(4) - 18*x^5)),x)

[Out]

int(-(exp(x)*(324*x^3*log(3) - 648*x^3*exp(4) - 144*x^3 + 54*x^4 + 18*x^5) - exp(3*x)*(648*x*exp(4) - 324*x*lo
g(3)) + exp(4*x)*(162*exp(4) - 81*log(3)) + 162*x^4*exp(4) - 81*x^4*log(3) + 36*x^4 - exp(2*x)*(486*x^2*log(3)
- 972*x^2*exp(4) - 108*x^2 + 54*x^3 + 18*x^4))/(81*x^4*log(3)^2 + exp(4*x)*(324*exp(8) - 324*exp(4)*log(3) +
81*log(3)^2) + exp(2*x)*(486*x^2*log(3)^2 - 36*x^3*exp(4) + 1944*x^2*exp(8) - log(3)*(1944*x^2*exp(4) - 18*x^3
)) - exp(3*x)*(1296*x*exp(8) + 324*x*log(3)^2 - 1296*x*exp(4)*log(3)) - 36*x^5*exp(4) + 324*x^4*exp(8) - exp(x
)*(324*x^3*log(3)^2 - 72*x^4*exp(4) + 1296*x^3*exp(8) - log(3)*(1296*x^3*exp(4) - 36*x^4)) + x^6 - log(3)*(324
*x^4*exp(4) - 18*x^5)), x)

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sympy [B]  time = 0.67, size = 119, normalized size = 4.25 \begin {gather*} - \frac {x}{- \log {\relax (3 )} + 2 e^{4}} + \frac {- x^{4} - 4 x^{3}}{- 2 x^{3} e^{4} + x^{3} \log {\relax (3 )} - 36 x^{2} e^{4} \log {\relax (3 )} + 9 x^{2} \log {\relax (3 )}^{2} + 36 x^{2} e^{8} + \left (- 72 x e^{8} - 18 x \log {\relax (3 )}^{2} + 72 x e^{4} \log {\relax (3 )}\right ) e^{x} + \left (- 36 e^{4} \log {\relax (3 )} + 9 \log {\relax (3 )}^{2} + 36 e^{8}\right ) e^{2 x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((81*ln(3)-162*exp(4))*exp(x)**4+(-324*x*ln(3)+648*x*exp(4))*exp(x)**3+(486*x**2*ln(3)-972*x**2*exp(
4)+18*x**4+54*x**3-108*x**2)*exp(x)**2+(-324*x**3*ln(3)+648*x**3*exp(4)-18*x**5-54*x**4+144*x**3)*exp(x)+81*x*
*4*ln(3)-162*x**4*exp(4)-36*x**4)/((81*ln(3)**2-324*exp(4)*ln(3)+324*exp(4)**2)*exp(x)**4+(-324*x*ln(3)**2+129
6*exp(4)*x*ln(3)-1296*x*exp(4)**2)*exp(x)**3+(486*x**2*ln(3)**2+(-1944*x**2*exp(4)+18*x**3)*ln(3)+1944*x**2*ex
p(4)**2-36*x**3*exp(4))*exp(x)**2+(-324*x**3*ln(3)**2+(1296*x**3*exp(4)-36*x**4)*ln(3)-1296*x**3*exp(4)**2+72*
x**4*exp(4))*exp(x)+81*x**4*ln(3)**2+(-324*x**4*exp(4)+18*x**5)*ln(3)+324*x**4*exp(4)**2-36*x**5*exp(4)+x**6),
x)

[Out]

-x/(-log(3) + 2*exp(4)) + (-x**4 - 4*x**3)/(-2*x**3*exp(4) + x**3*log(3) - 36*x**2*exp(4)*log(3) + 9*x**2*log(
3)**2 + 36*x**2*exp(8) + (-72*x*exp(8) - 18*x*log(3)**2 + 72*x*exp(4)*log(3))*exp(x) + (-36*exp(4)*log(3) + 9*
log(3)**2 + 36*exp(8))*exp(2*x))

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