3.63.59 \(\int \frac {24 e^2 x^4-e^{2+x} x^6-108 e^2 x^3 \log (x)+(-180 e^2 x^3+12 e^{2+x} x^5) \log ^2(x)+324 e^2 x^2 \log ^3(x)+(729 e^2 x^2-54 e^{2+x} x^4) \log ^4(x)+(-1620 e^2 x+108 e^{2+x} x^3) \log ^6(x)+(1215 e^2-81 e^{2+x} x^2) \log ^8(x)}{576 x^4+240 x^5+25 x^6+e^{2 x} x^6+e^x (48 x^5+10 x^6)+(-4320 x^3-2340 x^4-300 x^5-12 e^{2 x} x^5+e^x (-468 x^4-120 x^5)) \log ^2(x)+(14580 x^2+8910 x^3+1350 x^4+54 e^{2 x} x^4+e^x (1782 x^3+540 x^4)) \log ^4(x)+(-24300 x-16200 x^2-2700 x^3-108 e^{2 x} x^3+e^x (-3240 x^2-1080 x^3)) \log ^6(x)+(18225+12150 x+2025 x^2+81 e^{2 x} x^2+e^x (2430 x+810 x^2)) \log ^8(x)} \, dx\)

Optimal. Leaf size=31 \[ \frac {e^2}{5+e^x+\frac {15}{x}+\frac {9 x}{\left (-x+3 \log ^2(x)\right )^2}} \]

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Rubi [F]  time = 25.62, 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 {24 e^2 x^4-e^{2+x} x^6-108 e^2 x^3 \log (x)+\left (-180 e^2 x^3+12 e^{2+x} x^5\right ) \log ^2(x)+324 e^2 x^2 \log ^3(x)+\left (729 e^2 x^2-54 e^{2+x} x^4\right ) \log ^4(x)+\left (-1620 e^2 x+108 e^{2+x} x^3\right ) \log ^6(x)+\left (1215 e^2-81 e^{2+x} x^2\right ) \log ^8(x)}{576 x^4+240 x^5+25 x^6+e^{2 x} x^6+e^x \left (48 x^5+10 x^6\right )+\left (-4320 x^3-2340 x^4-300 x^5-12 e^{2 x} x^5+e^x \left (-468 x^4-120 x^5\right )\right ) \log ^2(x)+\left (14580 x^2+8910 x^3+1350 x^4+54 e^{2 x} x^4+e^x \left (1782 x^3+540 x^4\right )\right ) \log ^4(x)+\left (-24300 x-16200 x^2-2700 x^3-108 e^{2 x} x^3+e^x \left (-3240 x^2-1080 x^3\right )\right ) \log ^6(x)+\left (18225+12150 x+2025 x^2+81 e^{2 x} x^2+e^x \left (2430 x+810 x^2\right )\right ) \log ^8(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(24*E^2*x^4 - E^(2 + x)*x^6 - 108*E^2*x^3*Log[x] + (-180*E^2*x^3 + 12*E^(2 + x)*x^5)*Log[x]^2 + 324*E^2*x^
2*Log[x]^3 + (729*E^2*x^2 - 54*E^(2 + x)*x^4)*Log[x]^4 + (-1620*E^2*x + 108*E^(2 + x)*x^3)*Log[x]^6 + (1215*E^
2 - 81*E^(2 + x)*x^2)*Log[x]^8)/(576*x^4 + 240*x^5 + 25*x^6 + E^(2*x)*x^6 + E^x*(48*x^5 + 10*x^6) + (-4320*x^3
- 2340*x^4 - 300*x^5 - 12*E^(2*x)*x^5 + E^x*(-468*x^4 - 120*x^5))*Log[x]^2 + (14580*x^2 + 8910*x^3 + 1350*x^4
+ 54*E^(2*x)*x^4 + E^x*(1782*x^3 + 540*x^4))*Log[x]^4 + (-24300*x - 16200*x^2 - 2700*x^3 - 108*E^(2*x)*x^3 +
E^x*(-3240*x^2 - 1080*x^3))*Log[x]^6 + (18225 + 12150*x + 2025*x^2 + 81*E^(2*x)*x^2 + E^x*(2430*x + 810*x^2))*
Log[x]^8),x]

[Out]

24*E^2*Defer[Int][x^4/(x^2*(24 + (5 + E^x)*x) - 6*x*(15 + (5 + E^x)*x)*Log[x]^2 + 9*(15 + (5 + E^x)*x)*Log[x]^
4)^2, x] + 24*E^2*Defer[Int][x^5/(x^2*(24 + (5 + E^x)*x) - 6*x*(15 + (5 + E^x)*x)*Log[x]^2 + 9*(15 + (5 + E^x)
*x)*Log[x]^4)^2, x] + 5*E^2*Defer[Int][x^6/(x^2*(24 + (5 + E^x)*x) - 6*x*(15 + (5 + E^x)*x)*Log[x]^2 + 9*(15 +
(5 + E^x)*x)*Log[x]^4)^2, x] - 108*E^2*Defer[Int][(x^3*Log[x])/(x^2*(24 + (5 + E^x)*x) - 6*x*(15 + (5 + E^x)*
x)*Log[x]^2 + 9*(15 + (5 + E^x)*x)*Log[x]^4)^2, x] - 180*E^2*Defer[Int][(x^3*Log[x]^2)/(x^2*(24 + (5 + E^x)*x)
- 6*x*(15 + (5 + E^x)*x)*Log[x]^2 + 9*(15 + (5 + E^x)*x)*Log[x]^4)^2, x] - 234*E^2*Defer[Int][(x^4*Log[x]^2)/
(x^2*(24 + (5 + E^x)*x) - 6*x*(15 + (5 + E^x)*x)*Log[x]^2 + 9*(15 + (5 + E^x)*x)*Log[x]^4)^2, x] - 60*E^2*Defe
r[Int][(x^5*Log[x]^2)/(x^2*(24 + (5 + E^x)*x) - 6*x*(15 + (5 + E^x)*x)*Log[x]^2 + 9*(15 + (5 + E^x)*x)*Log[x]^
4)^2, x] + 324*E^2*Defer[Int][(x^2*Log[x]^3)/(x^2*(24 + (5 + E^x)*x) - 6*x*(15 + (5 + E^x)*x)*Log[x]^2 + 9*(15
+ (5 + E^x)*x)*Log[x]^4)^2, x] + 729*E^2*Defer[Int][(x^2*Log[x]^4)/(x^2*(24 + (5 + E^x)*x) - 6*x*(15 + (5 + E
^x)*x)*Log[x]^2 + 9*(15 + (5 + E^x)*x)*Log[x]^4)^2, x] + 891*E^2*Defer[Int][(x^3*Log[x]^4)/(x^2*(24 + (5 + E^x
)*x) - 6*x*(15 + (5 + E^x)*x)*Log[x]^2 + 9*(15 + (5 + E^x)*x)*Log[x]^4)^2, x] + 270*E^2*Defer[Int][(x^4*Log[x]
^4)/(x^2*(24 + (5 + E^x)*x) - 6*x*(15 + (5 + E^x)*x)*Log[x]^2 + 9*(15 + (5 + E^x)*x)*Log[x]^4)^2, x] - 1620*E^
2*Defer[Int][(x*Log[x]^6)/(x^2*(24 + (5 + E^x)*x) - 6*x*(15 + (5 + E^x)*x)*Log[x]^2 + 9*(15 + (5 + E^x)*x)*Log
[x]^4)^2, x] - 1620*E^2*Defer[Int][(x^2*Log[x]^6)/(x^2*(24 + (5 + E^x)*x) - 6*x*(15 + (5 + E^x)*x)*Log[x]^2 +
9*(15 + (5 + E^x)*x)*Log[x]^4)^2, x] - 540*E^2*Defer[Int][(x^3*Log[x]^6)/(x^2*(24 + (5 + E^x)*x) - 6*x*(15 + (
5 + E^x)*x)*Log[x]^2 + 9*(15 + (5 + E^x)*x)*Log[x]^4)^2, x] + 1215*E^2*Defer[Int][Log[x]^8/(x^2*(24 + (5 + E^x
)*x) - 6*x*(15 + (5 + E^x)*x)*Log[x]^2 + 9*(15 + (5 + E^x)*x)*Log[x]^4)^2, x] + 1215*E^2*Defer[Int][(x*Log[x]^
8)/(x^2*(24 + (5 + E^x)*x) - 6*x*(15 + (5 + E^x)*x)*Log[x]^2 + 9*(15 + (5 + E^x)*x)*Log[x]^4)^2, x] + 405*E^2*
Defer[Int][(x^2*Log[x]^8)/(x^2*(24 + (5 + E^x)*x) - 6*x*(15 + (5 + E^x)*x)*Log[x]^2 + 9*(15 + (5 + E^x)*x)*Log
[x]^4)^2, x] - E^2*Defer[Int][x^3/(x^2*(24 + (5 + E^x)*x) - 6*x*(15 + (5 + E^x)*x)*Log[x]^2 + 9*(15 + (5 + E^x
)*x)*Log[x]^4), x] + 6*E^2*Defer[Int][(x^2*Log[x]^2)/(x^2*(24 + (5 + E^x)*x) - 6*x*(15 + (5 + E^x)*x)*Log[x]^2
+ 9*(15 + (5 + E^x)*x)*Log[x]^4), x] - 9*E^2*Defer[Int][(x*Log[x]^4)/(x^2*(24 + (5 + E^x)*x) - 6*x*(15 + (5 +
E^x)*x)*Log[x]^2 + 9*(15 + (5 + E^x)*x)*Log[x]^4), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^2 \left (x-3 \log ^2(x)\right ) \left (-x^3 \left (-24+e^x x^2\right )-108 x^2 \log (x)+9 x^2 \left (-12+e^x x^2\right ) \log ^2(x)-27 x \left (-15+e^x x^2\right ) \log ^4(x)+27 \left (-15+e^x x^2\right ) \log ^6(x)\right )}{\left (x^2 \left (24+\left (5+e^x\right ) x\right )-6 x \left (15+\left (5+e^x\right ) x\right ) \log ^2(x)+9 \left (15+\left (5+e^x\right ) x\right ) \log ^4(x)\right )^2} \, dx\\ &=e^2 \int \frac {\left (x-3 \log ^2(x)\right ) \left (-x^3 \left (-24+e^x x^2\right )-108 x^2 \log (x)+9 x^2 \left (-12+e^x x^2\right ) \log ^2(x)-27 x \left (-15+e^x x^2\right ) \log ^4(x)+27 \left (-15+e^x x^2\right ) \log ^6(x)\right )}{\left (x^2 \left (24+\left (5+e^x\right ) x\right )-6 x \left (15+\left (5+e^x\right ) x\right ) \log ^2(x)+9 \left (15+\left (5+e^x\right ) x\right ) \log ^4(x)\right )^2} \, dx\\ &=e^2 \int \left (-\frac {x \left (x-3 \log ^2(x)\right )^2}{24 x^2+5 x^3+e^x x^3-90 x \log ^2(x)-30 x^2 \log ^2(x)-6 e^x x^2 \log ^2(x)+135 \log ^4(x)+45 x \log ^4(x)+9 e^x x \log ^4(x)}+\frac {24 x^4+24 x^5+5 x^6-108 x^3 \log (x)-180 x^3 \log ^2(x)-234 x^4 \log ^2(x)-60 x^5 \log ^2(x)+324 x^2 \log ^3(x)+729 x^2 \log ^4(x)+891 x^3 \log ^4(x)+270 x^4 \log ^4(x)-1620 x \log ^6(x)-1620 x^2 \log ^6(x)-540 x^3 \log ^6(x)+1215 \log ^8(x)+1215 x \log ^8(x)+405 x^2 \log ^8(x)}{\left (24 x^2+5 x^3+e^x x^3-90 x \log ^2(x)-30 x^2 \log ^2(x)-6 e^x x^2 \log ^2(x)+135 \log ^4(x)+45 x \log ^4(x)+9 e^x x \log ^4(x)\right )^2}\right ) \, dx\\ &=-\left (e^2 \int \frac {x \left (x-3 \log ^2(x)\right )^2}{24 x^2+5 x^3+e^x x^3-90 x \log ^2(x)-30 x^2 \log ^2(x)-6 e^x x^2 \log ^2(x)+135 \log ^4(x)+45 x \log ^4(x)+9 e^x x \log ^4(x)} \, dx\right )+e^2 \int \frac {24 x^4+24 x^5+5 x^6-108 x^3 \log (x)-180 x^3 \log ^2(x)-234 x^4 \log ^2(x)-60 x^5 \log ^2(x)+324 x^2 \log ^3(x)+729 x^2 \log ^4(x)+891 x^3 \log ^4(x)+270 x^4 \log ^4(x)-1620 x \log ^6(x)-1620 x^2 \log ^6(x)-540 x^3 \log ^6(x)+1215 \log ^8(x)+1215 x \log ^8(x)+405 x^2 \log ^8(x)}{\left (24 x^2+5 x^3+e^x x^3-90 x \log ^2(x)-30 x^2 \log ^2(x)-6 e^x x^2 \log ^2(x)+135 \log ^4(x)+45 x \log ^4(x)+9 e^x x \log ^4(x)\right )^2} \, dx\\ &=-\left (e^2 \int \frac {x \left (x-3 \log ^2(x)\right )^2}{x^2 \left (24+\left (5+e^x\right ) x\right )-6 x \left (15+\left (5+e^x\right ) x\right ) \log ^2(x)+9 \left (15+\left (5+e^x\right ) x\right ) \log ^4(x)} \, dx\right )+e^2 \int \frac {x^4 \left (24+24 x+5 x^2\right )-108 x^3 \log (x)-6 x^3 \left (30+39 x+10 x^2\right ) \log ^2(x)+324 x^2 \log ^3(x)+27 x^2 \left (27+33 x+10 x^2\right ) \log ^4(x)-540 x \left (3+3 x+x^2\right ) \log ^6(x)+405 \left (3+3 x+x^2\right ) \log ^8(x)}{\left (x^2 \left (24+\left (5+e^x\right ) x\right )-6 x \left (15+\left (5+e^x\right ) x\right ) \log ^2(x)+9 \left (15+\left (5+e^x\right ) x\right ) \log ^4(x)\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.39, size = 62, normalized size = 2.00 \begin {gather*} \frac {e^2 x \left (x-3 \log ^2(x)\right )^2}{x^2 \left (24+\left (5+e^x\right ) x\right )-6 x \left (15+\left (5+e^x\right ) x\right ) \log ^2(x)+9 \left (15+\left (5+e^x\right ) x\right ) \log ^4(x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(24*E^2*x^4 - E^(2 + x)*x^6 - 108*E^2*x^3*Log[x] + (-180*E^2*x^3 + 12*E^(2 + x)*x^5)*Log[x]^2 + 324*
E^2*x^2*Log[x]^3 + (729*E^2*x^2 - 54*E^(2 + x)*x^4)*Log[x]^4 + (-1620*E^2*x + 108*E^(2 + x)*x^3)*Log[x]^6 + (1
215*E^2 - 81*E^(2 + x)*x^2)*Log[x]^8)/(576*x^4 + 240*x^5 + 25*x^6 + E^(2*x)*x^6 + E^x*(48*x^5 + 10*x^6) + (-43
20*x^3 - 2340*x^4 - 300*x^5 - 12*E^(2*x)*x^5 + E^x*(-468*x^4 - 120*x^5))*Log[x]^2 + (14580*x^2 + 8910*x^3 + 13
50*x^4 + 54*E^(2*x)*x^4 + E^x*(1782*x^3 + 540*x^4))*Log[x]^4 + (-24300*x - 16200*x^2 - 2700*x^3 - 108*E^(2*x)*
x^3 + E^x*(-3240*x^2 - 1080*x^3))*Log[x]^6 + (18225 + 12150*x + 2025*x^2 + 81*E^(2*x)*x^2 + E^x*(2430*x + 810*
x^2))*Log[x]^8),x]

[Out]

(E^2*x*(x - 3*Log[x]^2)^2)/(x^2*(24 + (5 + E^x)*x) - 6*x*(15 + (5 + E^x)*x)*Log[x]^2 + 9*(15 + (5 + E^x)*x)*Lo
g[x]^4)

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fricas [B]  time = 1.24, size = 99, normalized size = 3.19 \begin {gather*} \frac {9 \, x e^{4} \log \relax (x)^{4} - 6 \, x^{2} e^{4} \log \relax (x)^{2} + x^{3} e^{4}}{9 \, {\left (5 \, {\left (x + 3\right )} e^{2} + x e^{\left (x + 2\right )}\right )} \log \relax (x)^{4} + x^{3} e^{\left (x + 2\right )} - 6 \, {\left (x^{2} e^{\left (x + 2\right )} + 5 \, {\left (x^{2} + 3 \, x\right )} e^{2}\right )} \log \relax (x)^{2} + {\left (5 \, x^{3} + 24 \, x^{2}\right )} e^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-81*x^2*exp(2)*exp(x)+1215*exp(2))*log(x)^8+(108*x^3*exp(2)*exp(x)-1620*exp(2)*x)*log(x)^6+(-54*x^
4*exp(2)*exp(x)+729*x^2*exp(2))*log(x)^4+324*x^2*exp(2)*log(x)^3+(12*x^5*exp(2)*exp(x)-180*x^3*exp(2))*log(x)^
2-108*x^3*exp(2)*log(x)-x^6*exp(2)*exp(x)+24*x^4*exp(2))/((81*exp(x)^2*x^2+(810*x^2+2430*x)*exp(x)+2025*x^2+12
150*x+18225)*log(x)^8+(-108*exp(x)^2*x^3+(-1080*x^3-3240*x^2)*exp(x)-2700*x^3-16200*x^2-24300*x)*log(x)^6+(54*
exp(x)^2*x^4+(540*x^4+1782*x^3)*exp(x)+1350*x^4+8910*x^3+14580*x^2)*log(x)^4+(-12*x^5*exp(x)^2+(-120*x^5-468*x
^4)*exp(x)-300*x^5-2340*x^4-4320*x^3)*log(x)^2+x^6*exp(x)^2+(10*x^6+48*x^5)*exp(x)+25*x^6+240*x^5+576*x^4),x,
algorithm="fricas")

[Out]

(9*x*e^4*log(x)^4 - 6*x^2*e^4*log(x)^2 + x^3*e^4)/(9*(5*(x + 3)*e^2 + x*e^(x + 2))*log(x)^4 + x^3*e^(x + 2) -
6*(x^2*e^(x + 2) + 5*(x^2 + 3*x)*e^2)*log(x)^2 + (5*x^3 + 24*x^2)*e^2)

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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*x^2*exp(2)*exp(x)+1215*exp(2))*log(x)^8+(108*x^3*exp(2)*exp(x)-1620*exp(2)*x)*log(x)^6+(-54*x^
4*exp(2)*exp(x)+729*x^2*exp(2))*log(x)^4+324*x^2*exp(2)*log(x)^3+(12*x^5*exp(2)*exp(x)-180*x^3*exp(2))*log(x)^
2-108*x^3*exp(2)*log(x)-x^6*exp(2)*exp(x)+24*x^4*exp(2))/((81*exp(x)^2*x^2+(810*x^2+2430*x)*exp(x)+2025*x^2+12
150*x+18225)*log(x)^8+(-108*exp(x)^2*x^3+(-1080*x^3-3240*x^2)*exp(x)-2700*x^3-16200*x^2-24300*x)*log(x)^6+(54*
exp(x)^2*x^4+(540*x^4+1782*x^3)*exp(x)+1350*x^4+8910*x^3+14580*x^2)*log(x)^4+(-12*x^5*exp(x)^2+(-120*x^5-468*x
^4)*exp(x)-300*x^5-2340*x^4-4320*x^3)*log(x)^2+x^6*exp(x)^2+(10*x^6+48*x^5)*exp(x)+25*x^6+240*x^5+576*x^4),x,
algorithm="giac")

[Out]

Timed out

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maple [B]  time = 0.14, size = 103, normalized size = 3.32

method	result	size
risch	\(\frac {{\mathrm e}^{2} x}{{\mathrm e}^{x} x +5 x +15}-\frac {9 x^{3} {\mathrm e}^{2}}{\left ({\mathrm e}^{x} x +5 x +15\right ) \left (9 x \ln \relax (x )^{4} {\mathrm e}^{x}+45 x \ln \relax (x )^{4}-6 x^{2} {\mathrm e}^{x} \ln \relax (x )^{2}+135 \ln \relax (x )^{4}-30 x^{2} \ln \relax (x )^{2}+{\mathrm e}^{x} x^{3}-90 x \ln \relax (x )^{2}+5 x^{3}+24 x^{2}\right )}\)	\(103\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-81*x^2*exp(2)*exp(x)+1215*exp(2))*ln(x)^8+(108*x^3*exp(2)*exp(x)-1620*exp(2)*x)*ln(x)^6+(-54*x^4*exp(2)
*exp(x)+729*x^2*exp(2))*ln(x)^4+324*x^2*exp(2)*ln(x)^3+(12*x^5*exp(2)*exp(x)-180*x^3*exp(2))*ln(x)^2-108*x^3*e
xp(2)*ln(x)-x^6*exp(2)*exp(x)+24*x^4*exp(2))/((81*exp(x)^2*x^2+(810*x^2+2430*x)*exp(x)+2025*x^2+12150*x+18225)
*ln(x)^8+(-108*exp(x)^2*x^3+(-1080*x^3-3240*x^2)*exp(x)-2700*x^3-16200*x^2-24300*x)*ln(x)^6+(54*exp(x)^2*x^4+(
540*x^4+1782*x^3)*exp(x)+1350*x^4+8910*x^3+14580*x^2)*ln(x)^4+(-12*x^5*exp(x)^2+(-120*x^5-468*x^4)*exp(x)-300*
x^5-2340*x^4-4320*x^3)*ln(x)^2+x^6*exp(x)^2+(10*x^6+48*x^5)*exp(x)+25*x^6+240*x^5+576*x^4),x,method=_RETURNVER
BOSE)

[Out]

exp(2)*x/(exp(x)*x+5*x+15)-9*x^3*exp(2)/(exp(x)*x+5*x+15)/(9*x*ln(x)^4*exp(x)+45*x*ln(x)^4-6*x^2*exp(x)*ln(x)^
2+135*ln(x)^4-30*x^2*ln(x)^2+exp(x)*x^3-90*x*ln(x)^2+5*x^3+24*x^2)

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maxima [B]  time = 0.66, size = 86, normalized size = 2.77 \begin {gather*} \frac {9 \, x e^{2} \log \relax (x)^{4} - 6 \, x^{2} e^{2} \log \relax (x)^{2} + x^{3} e^{2}}{45 \, {\left (x + 3\right )} \log \relax (x)^{4} + 5 \, x^{3} - 30 \, {\left (x^{2} + 3 \, x\right )} \log \relax (x)^{2} + 24 \, x^{2} + {\left (9 \, x \log \relax (x)^{4} - 6 \, x^{2} \log \relax (x)^{2} + x^{3}\right )} e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-81*x^2*exp(2)*exp(x)+1215*exp(2))*log(x)^8+(108*x^3*exp(2)*exp(x)-1620*exp(2)*x)*log(x)^6+(-54*x^
4*exp(2)*exp(x)+729*x^2*exp(2))*log(x)^4+324*x^2*exp(2)*log(x)^3+(12*x^5*exp(2)*exp(x)-180*x^3*exp(2))*log(x)^
2-108*x^3*exp(2)*log(x)-x^6*exp(2)*exp(x)+24*x^4*exp(2))/((81*exp(x)^2*x^2+(810*x^2+2430*x)*exp(x)+2025*x^2+12
150*x+18225)*log(x)^8+(-108*exp(x)^2*x^3+(-1080*x^3-3240*x^2)*exp(x)-2700*x^3-16200*x^2-24300*x)*log(x)^6+(54*
exp(x)^2*x^4+(540*x^4+1782*x^3)*exp(x)+1350*x^4+8910*x^3+14580*x^2)*log(x)^4+(-12*x^5*exp(x)^2+(-120*x^5-468*x
^4)*exp(x)-300*x^5-2340*x^4-4320*x^3)*log(x)^2+x^6*exp(x)^2+(10*x^6+48*x^5)*exp(x)+25*x^6+240*x^5+576*x^4),x,
algorithm="maxima")

[Out]

(9*x*e^2*log(x)^4 - 6*x^2*e^2*log(x)^2 + x^3*e^2)/(45*(x + 3)*log(x)^4 + 5*x^3 - 30*(x^2 + 3*x)*log(x)^2 + 24*
x^2 + (9*x*log(x)^4 - 6*x^2*log(x)^2 + x^3)*e^x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} -\int -\frac {{\ln \relax (x)}^2\,\left (12\,x^5\,{\mathrm {e}}^{x+2}-180\,x^3\,{\mathrm {e}}^2\right )-{\ln \relax (x)}^4\,\left (54\,x^4\,{\mathrm {e}}^{x+2}-729\,x^2\,{\mathrm {e}}^2\right )+{\ln \relax (x)}^8\,\left (1215\,{\mathrm {e}}^2-81\,x^2\,{\mathrm {e}}^{x+2}\right )-x^6\,{\mathrm {e}}^{x+2}+24\,x^4\,{\mathrm {e}}^2-{\ln \relax (x)}^6\,\left (1620\,x\,{\mathrm {e}}^2-108\,x^3\,{\mathrm {e}}^{x+2}\right )-108\,x^3\,{\mathrm {e}}^2\,\ln \relax (x)+324\,x^2\,{\mathrm {e}}^2\,{\ln \relax (x)}^3}{{\mathrm {e}}^x\,\left (10\,x^6+48\,x^5\right )-{\ln \relax (x)}^2\,\left ({\mathrm {e}}^x\,\left (120\,x^5+468\,x^4\right )+12\,x^5\,{\mathrm {e}}^{2\,x}+4320\,x^3+2340\,x^4+300\,x^5\right )+{\ln \relax (x)}^4\,\left ({\mathrm {e}}^x\,\left (540\,x^4+1782\,x^3\right )+54\,x^4\,{\mathrm {e}}^{2\,x}+14580\,x^2+8910\,x^3+1350\,x^4\right )+{\ln \relax (x)}^8\,\left (12150\,x+81\,x^2\,{\mathrm {e}}^{2\,x}+{\mathrm {e}}^x\,\left (810\,x^2+2430\,x\right )+2025\,x^2+18225\right )+x^6\,{\mathrm {e}}^{2\,x}-{\ln \relax (x)}^6\,\left (24300\,x+{\mathrm {e}}^x\,\left (1080\,x^3+3240\,x^2\right )+108\,x^3\,{\mathrm {e}}^{2\,x}+16200\,x^2+2700\,x^3\right )+576\,x^4+240\,x^5+25\,x^6} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x)^2*(180*x^3*exp(2) - 12*x^5*exp(2)*exp(x)) - log(x)^4*(729*x^2*exp(2) - 54*x^4*exp(2)*exp(x)) - lo
g(x)^8*(1215*exp(2) - 81*x^2*exp(2)*exp(x)) - 24*x^4*exp(2) + log(x)^6*(1620*x*exp(2) - 108*x^3*exp(2)*exp(x))
+ x^6*exp(2)*exp(x) + 108*x^3*exp(2)*log(x) - 324*x^2*exp(2)*log(x)^3)/(exp(x)*(48*x^5 + 10*x^6) - log(x)^2*(
exp(x)*(468*x^4 + 120*x^5) + 12*x^5*exp(2*x) + 4320*x^3 + 2340*x^4 + 300*x^5) + log(x)^4*(exp(x)*(1782*x^3 + 5
40*x^4) + 54*x^4*exp(2*x) + 14580*x^2 + 8910*x^3 + 1350*x^4) + log(x)^8*(12150*x + 81*x^2*exp(2*x) + exp(x)*(2
430*x + 810*x^2) + 2025*x^2 + 18225) + x^6*exp(2*x) - log(x)^6*(24300*x + exp(x)*(3240*x^2 + 1080*x^3) + 108*x
^3*exp(2*x) + 16200*x^2 + 2700*x^3) + 576*x^4 + 240*x^5 + 25*x^6),x)

[Out]

-int(-(log(x)^2*(12*x^5*exp(x + 2) - 180*x^3*exp(2)) - log(x)^4*(54*x^4*exp(x + 2) - 729*x^2*exp(2)) + log(x)^
8*(1215*exp(2) - 81*x^2*exp(x + 2)) - x^6*exp(x + 2) + 24*x^4*exp(2) - log(x)^6*(1620*x*exp(2) - 108*x^3*exp(x
+ 2)) - 108*x^3*exp(2)*log(x) + 324*x^2*exp(2)*log(x)^3)/(exp(x)*(48*x^5 + 10*x^6) - log(x)^2*(exp(x)*(468*x^
4 + 120*x^5) + 12*x^5*exp(2*x) + 4320*x^3 + 2340*x^4 + 300*x^5) + log(x)^4*(exp(x)*(1782*x^3 + 540*x^4) + 54*x
^4*exp(2*x) + 14580*x^2 + 8910*x^3 + 1350*x^4) + log(x)^8*(12150*x + 81*x^2*exp(2*x) + exp(x)*(2430*x + 810*x^
2) + 2025*x^2 + 18225) + x^6*exp(2*x) - log(x)^6*(24300*x + exp(x)*(3240*x^2 + 1080*x^3) + 108*x^3*exp(2*x) +
16200*x^2 + 2700*x^3) + 576*x^4 + 240*x^5 + 25*x^6), x)

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sympy [B]  time = 1.30, size = 100, normalized size = 3.23 \begin {gather*} \frac {x^{3} e^{2} - 6 x^{2} e^{2} \log {\relax (x )}^{2} + 9 x e^{2} \log {\relax (x )}^{4}}{5 x^{3} - 30 x^{2} \log {\relax (x )}^{2} + 24 x^{2} + 45 x \log {\relax (x )}^{4} - 90 x \log {\relax (x )}^{2} + \left (x^{3} - 6 x^{2} \log {\relax (x )}^{2} + 9 x \log {\relax (x )}^{4}\right ) e^{x} + 135 \log {\relax (x )}^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-81*x**2*exp(2)*exp(x)+1215*exp(2))*ln(x)**8+(108*x**3*exp(2)*exp(x)-1620*exp(2)*x)*ln(x)**6+(-54*
x**4*exp(2)*exp(x)+729*x**2*exp(2))*ln(x)**4+324*x**2*exp(2)*ln(x)**3+(12*x**5*exp(2)*exp(x)-180*x**3*exp(2))*
ln(x)**2-108*x**3*exp(2)*ln(x)-x**6*exp(2)*exp(x)+24*x**4*exp(2))/((81*exp(x)**2*x**2+(810*x**2+2430*x)*exp(x)
+2025*x**2+12150*x+18225)*ln(x)**8+(-108*exp(x)**2*x**3+(-1080*x**3-3240*x**2)*exp(x)-2700*x**3-16200*x**2-243
00*x)*ln(x)**6+(54*exp(x)**2*x**4+(540*x**4+1782*x**3)*exp(x)+1350*x**4+8910*x**3+14580*x**2)*ln(x)**4+(-12*x*
*5*exp(x)**2+(-120*x**5-468*x**4)*exp(x)-300*x**5-2340*x**4-4320*x**3)*ln(x)**2+x**6*exp(x)**2+(10*x**6+48*x**
5)*exp(x)+25*x**6+240*x**5+576*x**4),x)

[Out]

(x**3*exp(2) - 6*x**2*exp(2)*log(x)**2 + 9*x*exp(2)*log(x)**4)/(5*x**3 - 30*x**2*log(x)**2 + 24*x**2 + 45*x*lo
g(x)**4 - 90*x*log(x)**2 + (x**3 - 6*x**2*log(x)**2 + 9*x*log(x)**4)*exp(x) + 135*log(x)**4)

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