3.37.95 \(\int \frac {-x^5-3 x^6+e^x (-5 x^4+4 x^5)-8 x^4 \log (x)+5 x^4 \log ^2(x)}{-e^{5 x}-x^5+5 x^6-10 x^7+10 x^8-5 x^9+x^{10}+e^{4 x} (-5 x+5 x^2)+e^{3 x} (-10 x^2+20 x^3-10 x^4)+e^{2 x} (-10 x^3+30 x^4-30 x^5+10 x^6)+e^x (-5 x^4+20 x^5-30 x^6+20 x^7-5 x^8)+(5 e^{4 x}+5 x^4-20 x^5+30 x^6-20 x^7+5 x^8+e^{3 x} (20 x-20 x^2)+e^{2 x} (30 x^2-60 x^3+30 x^4)+e^x (20 x^3-60 x^4+60 x^5-20 x^6)) \log ^2(x)+(-10 e^{3 x}-10 x^3+30 x^4-30 x^5+10 x^6+e^{2 x} (-30 x+30 x^2)+e^x (-30 x^2+60 x^3-30 x^4)) \log ^4(x)+(10 e^{2 x}+10 x^2-20 x^3+10 x^4+e^x (20 x-20 x^2)) \log ^6(x)+(-5 e^x-5 x+5 x^2) \log ^8(x)+\log ^{10}(x)} \, dx\)

Optimal. Leaf size=22 \[ \frac {x^5}{\left (e^x+x-x^2-\log ^2(x)\right )^4} \]

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Rubi [F]  time = 11.29, 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 {-x^5-3 x^6+e^x \left (-5 x^4+4 x^5\right )-8 x^4 \log (x)+5 x^4 \log ^2(x)}{-e^{5 x}-x^5+5 x^6-10 x^7+10 x^8-5 x^9+x^{10}+e^{4 x} \left (-5 x+5 x^2\right )+e^{3 x} \left (-10 x^2+20 x^3-10 x^4\right )+e^{2 x} \left (-10 x^3+30 x^4-30 x^5+10 x^6\right )+e^x \left (-5 x^4+20 x^5-30 x^6+20 x^7-5 x^8\right )+\left (5 e^{4 x}+5 x^4-20 x^5+30 x^6-20 x^7+5 x^8+e^{3 x} \left (20 x-20 x^2\right )+e^{2 x} \left (30 x^2-60 x^3+30 x^4\right )+e^x \left (20 x^3-60 x^4+60 x^5-20 x^6\right )\right ) \log ^2(x)+\left (-10 e^{3 x}-10 x^3+30 x^4-30 x^5+10 x^6+e^{2 x} \left (-30 x+30 x^2\right )+e^x \left (-30 x^2+60 x^3-30 x^4\right )\right ) \log ^4(x)+\left (10 e^{2 x}+10 x^2-20 x^3+10 x^4+e^x \left (20 x-20 x^2\right )\right ) \log ^6(x)+\left (-5 e^x-5 x+5 x^2\right ) \log ^8(x)+\log ^{10}(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-x^5 - 3*x^6 + E^x*(-5*x^4 + 4*x^5) - 8*x^4*Log[x] + 5*x^4*Log[x]^2)/(-E^(5*x) - x^5 + 5*x^6 - 10*x^7 + 1
0*x^8 - 5*x^9 + x^10 + E^(4*x)*(-5*x + 5*x^2) + E^(3*x)*(-10*x^2 + 20*x^3 - 10*x^4) + E^(2*x)*(-10*x^3 + 30*x^
4 - 30*x^5 + 10*x^6) + E^x*(-5*x^4 + 20*x^5 - 30*x^6 + 20*x^7 - 5*x^8) + (5*E^(4*x) + 5*x^4 - 20*x^5 + 30*x^6
- 20*x^7 + 5*x^8 + E^(3*x)*(20*x - 20*x^2) + E^(2*x)*(30*x^2 - 60*x^3 + 30*x^4) + E^x*(20*x^3 - 60*x^4 + 60*x^
5 - 20*x^6))*Log[x]^2 + (-10*E^(3*x) - 10*x^3 + 30*x^4 - 30*x^5 + 10*x^6 + E^(2*x)*(-30*x + 30*x^2) + E^x*(-30
*x^2 + 60*x^3 - 30*x^4))*Log[x]^4 + (10*E^(2*x) + 10*x^2 - 20*x^3 + 10*x^4 + E^x*(20*x - 20*x^2))*Log[x]^6 + (
-5*E^x - 5*x + 5*x^2)*Log[x]^8 + Log[x]^10),x]

[Out]

4*Defer[Int][x^5/(-E^x - x + x^2 + Log[x]^2)^5, x] - 12*Defer[Int][x^6/(-E^x - x + x^2 + Log[x]^2)^5, x] + 4*D
efer[Int][x^7/(-E^x - x + x^2 + Log[x]^2)^5, x] - 8*Defer[Int][(x^4*Log[x])/(-E^x - x + x^2 + Log[x]^2)^5, x]
+ 4*Defer[Int][(x^5*Log[x]^2)/(-E^x - x + x^2 + Log[x]^2)^5, x] + 5*Defer[Int][x^4/(-E^x - x + x^2 + Log[x]^2)
^4, x] - 4*Defer[Int][x^5/(-E^x - x + x^2 + Log[x]^2)^4, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x^4 \left (e^x (5-4 x)+x (1+3 x)+8 \log (x)-5 \log ^2(x)\right )}{\left (e^x-(-1+x) x-\log ^2(x)\right )^5} \, dx\\ &=\int \left (-\frac {x^4 (-5+4 x)}{\left (-e^x-x+x^2+\log ^2(x)\right )^4}+\frac {4 x^4 \left (x-3 x^2+x^3-2 \log (x)+x \log ^2(x)\right )}{\left (-e^x-x+x^2+\log ^2(x)\right )^5}\right ) \, dx\\ &=4 \int \frac {x^4 \left (x-3 x^2+x^3-2 \log (x)+x \log ^2(x)\right )}{\left (-e^x-x+x^2+\log ^2(x)\right )^5} \, dx-\int \frac {x^4 (-5+4 x)}{\left (-e^x-x+x^2+\log ^2(x)\right )^4} \, dx\\ &=4 \int \left (\frac {x^5}{\left (-e^x-x+x^2+\log ^2(x)\right )^5}-\frac {3 x^6}{\left (-e^x-x+x^2+\log ^2(x)\right )^5}+\frac {x^7}{\left (-e^x-x+x^2+\log ^2(x)\right )^5}-\frac {2 x^4 \log (x)}{\left (-e^x-x+x^2+\log ^2(x)\right )^5}+\frac {x^5 \log ^2(x)}{\left (-e^x-x+x^2+\log ^2(x)\right )^5}\right ) \, dx-\int \left (-\frac {5 x^4}{\left (-e^x-x+x^2+\log ^2(x)\right )^4}+\frac {4 x^5}{\left (-e^x-x+x^2+\log ^2(x)\right )^4}\right ) \, dx\\ &=4 \int \frac {x^5}{\left (-e^x-x+x^2+\log ^2(x)\right )^5} \, dx+4 \int \frac {x^7}{\left (-e^x-x+x^2+\log ^2(x)\right )^5} \, dx+4 \int \frac {x^5 \log ^2(x)}{\left (-e^x-x+x^2+\log ^2(x)\right )^5} \, dx-4 \int \frac {x^5}{\left (-e^x-x+x^2+\log ^2(x)\right )^4} \, dx+5 \int \frac {x^4}{\left (-e^x-x+x^2+\log ^2(x)\right )^4} \, dx-8 \int \frac {x^4 \log (x)}{\left (-e^x-x+x^2+\log ^2(x)\right )^5} \, dx-12 \int \frac {x^6}{\left (-e^x-x+x^2+\log ^2(x)\right )^5} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.79, size = 22, normalized size = 1.00 \begin {gather*} \frac {x^5}{\left (-e^x-x+x^2+\log ^2(x)\right )^4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-x^5 - 3*x^6 + E^x*(-5*x^4 + 4*x^5) - 8*x^4*Log[x] + 5*x^4*Log[x]^2)/(-E^(5*x) - x^5 + 5*x^6 - 10*x
^7 + 10*x^8 - 5*x^9 + x^10 + E^(4*x)*(-5*x + 5*x^2) + E^(3*x)*(-10*x^2 + 20*x^3 - 10*x^4) + E^(2*x)*(-10*x^3 +
30*x^4 - 30*x^5 + 10*x^6) + E^x*(-5*x^4 + 20*x^5 - 30*x^6 + 20*x^7 - 5*x^8) + (5*E^(4*x) + 5*x^4 - 20*x^5 + 3
0*x^6 - 20*x^7 + 5*x^8 + E^(3*x)*(20*x - 20*x^2) + E^(2*x)*(30*x^2 - 60*x^3 + 30*x^4) + E^x*(20*x^3 - 60*x^4 +
60*x^5 - 20*x^6))*Log[x]^2 + (-10*E^(3*x) - 10*x^3 + 30*x^4 - 30*x^5 + 10*x^6 + E^(2*x)*(-30*x + 30*x^2) + E^
x*(-30*x^2 + 60*x^3 - 30*x^4))*Log[x]^4 + (10*E^(2*x) + 10*x^2 - 20*x^3 + 10*x^4 + E^x*(20*x - 20*x^2))*Log[x]
^6 + (-5*E^x - 5*x + 5*x^2)*Log[x]^8 + Log[x]^10),x]

[Out]

x^5/(-E^x - x + x^2 + Log[x]^2)^4

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fricas [B]  time = 0.63, size = 200, normalized size = 9.09 \begin {gather*} \frac {x^{5}}{x^{8} + \log \relax (x)^{8} - 4 \, x^{7} + 4 \, {\left (x^{2} - x - e^{x}\right )} \log \relax (x)^{6} + 6 \, x^{6} - 4 \, x^{5} + 6 \, {\left (x^{4} - 2 \, x^{3} + x^{2} - 2 \, {\left (x^{2} - x\right )} e^{x} + e^{\left (2 \, x\right )}\right )} \log \relax (x)^{4} + x^{4} + 4 \, {\left (x^{6} - 3 \, x^{5} + 3 \, x^{4} - x^{3} + 3 \, {\left (x^{2} - x\right )} e^{\left (2 \, x\right )} - 3 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{x} - e^{\left (3 \, x\right )}\right )} \log \relax (x)^{2} - 4 \, {\left (x^{2} - x\right )} e^{\left (3 \, x\right )} + 6 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{6} - 3 \, x^{5} + 3 \, x^{4} - x^{3}\right )} e^{x} + e^{\left (4 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((5*x^4*log(x)^2-8*x^4*log(x)+(4*x^5-5*x^4)*exp(x)-3*x^6-x^5)/(log(x)^10+(-5*exp(x)+5*x^2-5*x)*log(x)
^8+(10*exp(x)^2+(-20*x^2+20*x)*exp(x)+10*x^4-20*x^3+10*x^2)*log(x)^6+(-10*exp(x)^3+(30*x^2-30*x)*exp(x)^2+(-30
*x^4+60*x^3-30*x^2)*exp(x)+10*x^6-30*x^5+30*x^4-10*x^3)*log(x)^4+(5*exp(x)^4+(-20*x^2+20*x)*exp(x)^3+(30*x^4-6
0*x^3+30*x^2)*exp(x)^2+(-20*x^6+60*x^5-60*x^4+20*x^3)*exp(x)+5*x^8-20*x^7+30*x^6-20*x^5+5*x^4)*log(x)^2-exp(x)
^5+(5*x^2-5*x)*exp(x)^4+(-10*x^4+20*x^3-10*x^2)*exp(x)^3+(10*x^6-30*x^5+30*x^4-10*x^3)*exp(x)^2+(-5*x^8+20*x^7
-30*x^6+20*x^5-5*x^4)*exp(x)+x^10-5*x^9+10*x^8-10*x^7+5*x^6-x^5),x, algorithm="fricas")

[Out]

x^5/(x^8 + log(x)^8 - 4*x^7 + 4*(x^2 - x - e^x)*log(x)^6 + 6*x^6 - 4*x^5 + 6*(x^4 - 2*x^3 + x^2 - 2*(x^2 - x)*
e^x + e^(2*x))*log(x)^4 + x^4 + 4*(x^6 - 3*x^5 + 3*x^4 - x^3 + 3*(x^2 - x)*e^(2*x) - 3*(x^4 - 2*x^3 + x^2)*e^x
- e^(3*x))*log(x)^2 - 4*(x^2 - x)*e^(3*x) + 6*(x^4 - 2*x^3 + x^2)*e^(2*x) - 4*(x^6 - 3*x^5 + 3*x^4 - x^3)*e^x
+ e^(4*x))

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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((5*x^4*log(x)^2-8*x^4*log(x)+(4*x^5-5*x^4)*exp(x)-3*x^6-x^5)/(log(x)^10+(-5*exp(x)+5*x^2-5*x)*log(x)
^8+(10*exp(x)^2+(-20*x^2+20*x)*exp(x)+10*x^4-20*x^3+10*x^2)*log(x)^6+(-10*exp(x)^3+(30*x^2-30*x)*exp(x)^2+(-30
*x^4+60*x^3-30*x^2)*exp(x)+10*x^6-30*x^5+30*x^4-10*x^3)*log(x)^4+(5*exp(x)^4+(-20*x^2+20*x)*exp(x)^3+(30*x^4-6
0*x^3+30*x^2)*exp(x)^2+(-20*x^6+60*x^5-60*x^4+20*x^3)*exp(x)+5*x^8-20*x^7+30*x^6-20*x^5+5*x^4)*log(x)^2-exp(x)
^5+(5*x^2-5*x)*exp(x)^4+(-10*x^4+20*x^3-10*x^2)*exp(x)^3+(10*x^6-30*x^5+30*x^4-10*x^3)*exp(x)^2+(-5*x^8+20*x^7
-30*x^6+20*x^5-5*x^4)*exp(x)+x^10-5*x^9+10*x^8-10*x^7+5*x^6-x^5),x, algorithm="giac")

[Out]

Timed out

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maple [A]  time = 0.09, size = 22, normalized size = 1.00

method	result	size
risch	\(\frac {x^{5}}{\left (\ln \relax (x )^{2}+x^{2}-{\mathrm e}^{x}-x \right )^{4}}\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((5*x^4*ln(x)^2-8*x^4*ln(x)+(4*x^5-5*x^4)*exp(x)-3*x^6-x^5)/(ln(x)^10+(-5*exp(x)+5*x^2-5*x)*ln(x)^8+(10*exp
(x)^2+(-20*x^2+20*x)*exp(x)+10*x^4-20*x^3+10*x^2)*ln(x)^6+(-10*exp(x)^3+(30*x^2-30*x)*exp(x)^2+(-30*x^4+60*x^3
-30*x^2)*exp(x)+10*x^6-30*x^5+30*x^4-10*x^3)*ln(x)^4+(5*exp(x)^4+(-20*x^2+20*x)*exp(x)^3+(30*x^4-60*x^3+30*x^2
)*exp(x)^2+(-20*x^6+60*x^5-60*x^4+20*x^3)*exp(x)+5*x^8-20*x^7+30*x^6-20*x^5+5*x^4)*ln(x)^2-exp(x)^5+(5*x^2-5*x
)*exp(x)^4+(-10*x^4+20*x^3-10*x^2)*exp(x)^3+(10*x^6-30*x^5+30*x^4-10*x^3)*exp(x)^2+(-5*x^8+20*x^7-30*x^6+20*x^
5-5*x^4)*exp(x)+x^10-5*x^9+10*x^8-10*x^7+5*x^6-x^5),x,method=_RETURNVERBOSE)

[Out]

x^5/(ln(x)^2+x^2-exp(x)-x)^4

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maxima [B]  time = 1.46, size = 202, normalized size = 9.18 \begin {gather*} \frac {x^{5}}{x^{8} + \log \relax (x)^{8} - 4 \, x^{7} + 4 \, {\left (x^{2} - x\right )} \log \relax (x)^{6} + 6 \, x^{6} - 4 \, x^{5} + 6 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} \log \relax (x)^{4} + x^{4} + 4 \, {\left (x^{6} - 3 \, x^{5} + 3 \, x^{4} - x^{3}\right )} \log \relax (x)^{2} - 4 \, {\left (x^{2} + \log \relax (x)^{2} - x\right )} e^{\left (3 \, x\right )} + 6 \, {\left (x^{4} + \log \relax (x)^{4} - 2 \, x^{3} + 2 \, {\left (x^{2} - x\right )} \log \relax (x)^{2} + x^{2}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{6} + \log \relax (x)^{6} - 3 \, x^{5} + 3 \, {\left (x^{2} - x\right )} \log \relax (x)^{4} + 3 \, x^{4} - x^{3} + 3 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} \log \relax (x)^{2}\right )} e^{x} + e^{\left (4 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((5*x^4*log(x)^2-8*x^4*log(x)+(4*x^5-5*x^4)*exp(x)-3*x^6-x^5)/(log(x)^10+(-5*exp(x)+5*x^2-5*x)*log(x)
^8+(10*exp(x)^2+(-20*x^2+20*x)*exp(x)+10*x^4-20*x^3+10*x^2)*log(x)^6+(-10*exp(x)^3+(30*x^2-30*x)*exp(x)^2+(-30
*x^4+60*x^3-30*x^2)*exp(x)+10*x^6-30*x^5+30*x^4-10*x^3)*log(x)^4+(5*exp(x)^4+(-20*x^2+20*x)*exp(x)^3+(30*x^4-6
0*x^3+30*x^2)*exp(x)^2+(-20*x^6+60*x^5-60*x^4+20*x^3)*exp(x)+5*x^8-20*x^7+30*x^6-20*x^5+5*x^4)*log(x)^2-exp(x)
^5+(5*x^2-5*x)*exp(x)^4+(-10*x^4+20*x^3-10*x^2)*exp(x)^3+(10*x^6-30*x^5+30*x^4-10*x^3)*exp(x)^2+(-5*x^8+20*x^7
-30*x^6+20*x^5-5*x^4)*exp(x)+x^10-5*x^9+10*x^8-10*x^7+5*x^6-x^5),x, algorithm="maxima")

[Out]

x^5/(x^8 + log(x)^8 - 4*x^7 + 4*(x^2 - x)*log(x)^6 + 6*x^6 - 4*x^5 + 6*(x^4 - 2*x^3 + x^2)*log(x)^4 + x^4 + 4*
(x^6 - 3*x^5 + 3*x^4 - x^3)*log(x)^2 - 4*(x^2 + log(x)^2 - x)*e^(3*x) + 6*(x^4 + log(x)^4 - 2*x^3 + 2*(x^2 - x
)*log(x)^2 + x^2)*e^(2*x) - 4*(x^6 + log(x)^6 - 3*x^5 + 3*(x^2 - x)*log(x)^4 + 3*x^4 - x^3 + 3*(x^4 - 2*x^3 +
x^2)*log(x)^2)*e^x + e^(4*x))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {{\mathrm {e}}^x\,\left (5\,x^4-4\,x^5\right )+8\,x^4\,\ln \relax (x)-5\,x^4\,{\ln \relax (x)}^2+x^5+3\,x^6}{{\mathrm {e}}^{5\,x}+{\mathrm {e}}^{4\,x}\,\left (5\,x-5\,x^2\right )-{\ln \relax (x)}^{10}+{\ln \relax (x)}^8\,\left (5\,x+5\,{\mathrm {e}}^x-5\,x^2\right )+{\mathrm {e}}^{3\,x}\,\left (10\,x^4-20\,x^3+10\,x^2\right )+{\mathrm {e}}^x\,\left (5\,x^8-20\,x^7+30\,x^6-20\,x^5+5\,x^4\right )+{\ln \relax (x)}^4\,\left (10\,{\mathrm {e}}^{3\,x}+{\mathrm {e}}^{2\,x}\,\left (30\,x-30\,x^2\right )+{\mathrm {e}}^x\,\left (30\,x^4-60\,x^3+30\,x^2\right )+10\,x^3-30\,x^4+30\,x^5-10\,x^6\right )-{\ln \relax (x)}^2\,\left (5\,{\mathrm {e}}^{4\,x}+{\mathrm {e}}^{3\,x}\,\left (20\,x-20\,x^2\right )+{\mathrm {e}}^x\,\left (-20\,x^6+60\,x^5-60\,x^4+20\,x^3\right )+{\mathrm {e}}^{2\,x}\,\left (30\,x^4-60\,x^3+30\,x^2\right )+5\,x^4-20\,x^5+30\,x^6-20\,x^7+5\,x^8\right )+{\mathrm {e}}^{2\,x}\,\left (-10\,x^6+30\,x^5-30\,x^4+10\,x^3\right )+x^5-5\,x^6+10\,x^7-10\,x^8+5\,x^9-x^{10}-{\ln \relax (x)}^6\,\left (10\,{\mathrm {e}}^{2\,x}+{\mathrm {e}}^x\,\left (20\,x-20\,x^2\right )+10\,x^2-20\,x^3+10\,x^4\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x)*(5*x^4 - 4*x^5) + 8*x^4*log(x) - 5*x^4*log(x)^2 + x^5 + 3*x^6)/(exp(5*x) + exp(4*x)*(5*x - 5*x^2)
- log(x)^10 + log(x)^8*(5*x + 5*exp(x) - 5*x^2) + exp(3*x)*(10*x^2 - 20*x^3 + 10*x^4) + exp(x)*(5*x^4 - 20*x^5
+ 30*x^6 - 20*x^7 + 5*x^8) + log(x)^4*(10*exp(3*x) + exp(2*x)*(30*x - 30*x^2) + exp(x)*(30*x^2 - 60*x^3 + 30*
x^4) + 10*x^3 - 30*x^4 + 30*x^5 - 10*x^6) - log(x)^2*(5*exp(4*x) + exp(3*x)*(20*x - 20*x^2) + exp(x)*(20*x^3 -
60*x^4 + 60*x^5 - 20*x^6) + exp(2*x)*(30*x^2 - 60*x^3 + 30*x^4) + 5*x^4 - 20*x^5 + 30*x^6 - 20*x^7 + 5*x^8) +
exp(2*x)*(10*x^3 - 30*x^4 + 30*x^5 - 10*x^6) + x^5 - 5*x^6 + 10*x^7 - 10*x^8 + 5*x^9 - x^10 - log(x)^6*(10*ex
p(2*x) + exp(x)*(20*x - 20*x^2) + 10*x^2 - 20*x^3 + 10*x^4)),x)

[Out]

int((exp(x)*(5*x^4 - 4*x^5) + 8*x^4*log(x) - 5*x^4*log(x)^2 + x^5 + 3*x^6)/(exp(5*x) + exp(4*x)*(5*x - 5*x^2)
- log(x)^10 + log(x)^8*(5*x + 5*exp(x) - 5*x^2) + exp(3*x)*(10*x^2 - 20*x^3 + 10*x^4) + exp(x)*(5*x^4 - 20*x^5
+ 30*x^6 - 20*x^7 + 5*x^8) + log(x)^4*(10*exp(3*x) + exp(2*x)*(30*x - 30*x^2) + exp(x)*(30*x^2 - 60*x^3 + 30*
x^4) + 10*x^3 - 30*x^4 + 30*x^5 - 10*x^6) - log(x)^2*(5*exp(4*x) + exp(3*x)*(20*x - 20*x^2) + exp(x)*(20*x^3 -
60*x^4 + 60*x^5 - 20*x^6) + exp(2*x)*(30*x^2 - 60*x^3 + 30*x^4) + 5*x^4 - 20*x^5 + 30*x^6 - 20*x^7 + 5*x^8) +
exp(2*x)*(10*x^3 - 30*x^4 + 30*x^5 - 10*x^6) + x^5 - 5*x^6 + 10*x^7 - 10*x^8 + 5*x^9 - x^10 - log(x)^6*(10*ex
p(2*x) + exp(x)*(20*x - 20*x^2) + 10*x^2 - 20*x^3 + 10*x^4)), x)

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sympy [B]  time = 0.98, size = 270, normalized size = 12.27 \begin {gather*} \frac {x^{5}}{x^{8} - 4 x^{7} + 4 x^{6} \log {\relax (x )}^{2} + 6 x^{6} - 12 x^{5} \log {\relax (x )}^{2} - 4 x^{5} + 6 x^{4} \log {\relax (x )}^{4} + 12 x^{4} \log {\relax (x )}^{2} + x^{4} - 12 x^{3} \log {\relax (x )}^{4} - 4 x^{3} \log {\relax (x )}^{2} + 4 x^{2} \log {\relax (x )}^{6} + 6 x^{2} \log {\relax (x )}^{4} - 4 x \log {\relax (x )}^{6} + \left (- 4 x^{2} + 4 x - 4 \log {\relax (x )}^{2}\right ) e^{3 x} + \left (6 x^{4} - 12 x^{3} + 12 x^{2} \log {\relax (x )}^{2} + 6 x^{2} - 12 x \log {\relax (x )}^{2} + 6 \log {\relax (x )}^{4}\right ) e^{2 x} + \left (- 4 x^{6} + 12 x^{5} - 12 x^{4} \log {\relax (x )}^{2} - 12 x^{4} + 24 x^{3} \log {\relax (x )}^{2} + 4 x^{3} - 12 x^{2} \log {\relax (x )}^{4} - 12 x^{2} \log {\relax (x )}^{2} + 12 x \log {\relax (x )}^{4} - 4 \log {\relax (x )}^{6}\right ) e^{x} + e^{4 x} + \log {\relax (x )}^{8}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((5*x**4*ln(x)**2-8*x**4*ln(x)+(4*x**5-5*x**4)*exp(x)-3*x**6-x**5)/(ln(x)**10+(-5*exp(x)+5*x**2-5*x)*
ln(x)**8+(10*exp(x)**2+(-20*x**2+20*x)*exp(x)+10*x**4-20*x**3+10*x**2)*ln(x)**6+(-10*exp(x)**3+(30*x**2-30*x)*
exp(x)**2+(-30*x**4+60*x**3-30*x**2)*exp(x)+10*x**6-30*x**5+30*x**4-10*x**3)*ln(x)**4+(5*exp(x)**4+(-20*x**2+2
0*x)*exp(x)**3+(30*x**4-60*x**3+30*x**2)*exp(x)**2+(-20*x**6+60*x**5-60*x**4+20*x**3)*exp(x)+5*x**8-20*x**7+30
*x**6-20*x**5+5*x**4)*ln(x)**2-exp(x)**5+(5*x**2-5*x)*exp(x)**4+(-10*x**4+20*x**3-10*x**2)*exp(x)**3+(10*x**6-
30*x**5+30*x**4-10*x**3)*exp(x)**2+(-5*x**8+20*x**7-30*x**6+20*x**5-5*x**4)*exp(x)+x**10-5*x**9+10*x**8-10*x**
7+5*x**6-x**5),x)

[Out]

x**5/(x**8 - 4*x**7 + 4*x**6*log(x)**2 + 6*x**6 - 12*x**5*log(x)**2 - 4*x**5 + 6*x**4*log(x)**4 + 12*x**4*log(
x)**2 + x**4 - 12*x**3*log(x)**4 - 4*x**3*log(x)**2 + 4*x**2*log(x)**6 + 6*x**2*log(x)**4 - 4*x*log(x)**6 + (-
4*x**2 + 4*x - 4*log(x)**2)*exp(3*x) + (6*x**4 - 12*x**3 + 12*x**2*log(x)**2 + 6*x**2 - 12*x*log(x)**2 + 6*log
(x)**4)*exp(2*x) + (-4*x**6 + 12*x**5 - 12*x**4*log(x)**2 - 12*x**4 + 24*x**3*log(x)**2 + 4*x**3 - 12*x**2*log
(x)**4 - 12*x**2*log(x)**2 + 12*x*log(x)**4 - 4*log(x)**6)*exp(x) + exp(4*x) + log(x)**8)

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