3.78.5 \(\int \frac {e^{\frac {x^4-4 x^6+4 x^7+4 x^8-8 x^9+4 x^{10}+(2 x^4-2 x^5-4 x^6+8 x^7-4 x^8) \log (x)+(x^4-2 x^5+x^6) \log ^2(x)}{4 x^4-4 x^2 \log (x)+\log ^2(x)}} (-2 x^3+4 x^5-4 x^6+16 x^7-24 x^8-32 x^9+80 x^{10}-48 x^{11}+(2 x^3+2 x^4-24 x^5+32 x^6+48 x^7-120 x^8+72 x^9) \log (x)+(8 x^3-10 x^4-24 x^5+60 x^6-36 x^7) \log ^2(x)+(4 x^3-10 x^4+6 x^5) \log ^3(x))}{-8 x^6+12 x^4 \log (x)-6 x^2 \log ^2(x)+\log ^3(x)} \, dx\)

Optimal. Leaf size=35 \[ e^{\left (-x^2+(2-x) x^2-\frac {x}{2 x-\frac {\log (x)}{x}}\right )^2} \]

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Rubi [F]  time = 80.25, 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 {\exp \left (\frac {x^4-4 x^6+4 x^7+4 x^8-8 x^9+4 x^{10}+\left (2 x^4-2 x^5-4 x^6+8 x^7-4 x^8\right ) \log (x)+\left (x^4-2 x^5+x^6\right ) \log ^2(x)}{4 x^4-4 x^2 \log (x)+\log ^2(x)}\right ) \left (-2 x^3+4 x^5-4 x^6+16 x^7-24 x^8-32 x^9+80 x^{10}-48 x^{11}+\left (2 x^3+2 x^4-24 x^5+32 x^6+48 x^7-120 x^8+72 x^9\right ) \log (x)+\left (8 x^3-10 x^4-24 x^5+60 x^6-36 x^7\right ) \log ^2(x)+\left (4 x^3-10 x^4+6 x^5\right ) \log ^3(x)\right )}{-8 x^6+12 x^4 \log (x)-6 x^2 \log ^2(x)+\log ^3(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((x^4 - 4*x^6 + 4*x^7 + 4*x^8 - 8*x^9 + 4*x^10 + (2*x^4 - 2*x^5 - 4*x^6 + 8*x^7 - 4*x^8)*Log[x] + (x^4
- 2*x^5 + x^6)*Log[x]^2)/(4*x^4 - 4*x^2*Log[x] + Log[x]^2))*(-2*x^3 + 4*x^5 - 4*x^6 + 16*x^7 - 24*x^8 - 32*x^9
+ 80*x^10 - 48*x^11 + (2*x^3 + 2*x^4 - 24*x^5 + 32*x^6 + 48*x^7 - 120*x^8 + 72*x^9)*Log[x] + (8*x^3 - 10*x^4
- 24*x^5 + 60*x^6 - 36*x^7)*Log[x]^2 + (4*x^3 - 10*x^4 + 6*x^5)*Log[x]^3))/(-8*x^6 + 12*x^4*Log[x] - 6*x^2*Log
[x]^2 + Log[x]^3),x]

[Out]

4*Defer[Int][E^((x^4*(1 - 2*x^2 + 2*x^3 + Log[x] - x*Log[x])^2)/(2*x^2 - Log[x])^2)*x^3, x] - 10*Defer[Int][E^
((x^4*(1 - 2*x^2 + 2*x^3 + Log[x] - x*Log[x])^2)/(2*x^2 - Log[x])^2)*x^4, x] + 6*Defer[Int][E^((x^4*(1 - 2*x^2
+ 2*x^3 + Log[x] - x*Log[x])^2)/(2*x^2 - Log[x])^2)*x^5, x] + 2*Defer[Int][(E^((x^4*(1 - 2*x^2 + 2*x^3 + Log[
x] - x*Log[x])^2)/(2*x^2 - Log[x])^2)*x^3)/(2*x^2 - Log[x])^3, x] - 8*Defer[Int][(E^((x^4*(1 - 2*x^2 + 2*x^3 +
Log[x] - x*Log[x])^2)/(2*x^2 - Log[x])^2)*x^5)/(2*x^2 - Log[x])^3, x] + 2*Defer[Int][(E^((x^4*(1 - 2*x^2 + 2*
x^3 + Log[x] - x*Log[x])^2)/(2*x^2 - Log[x])^2)*x^3)/(2*x^2 - Log[x])^2, x] + 2*Defer[Int][(E^((x^4*(1 - 2*x^2
+ 2*x^3 + Log[x] - x*Log[x])^2)/(2*x^2 - Log[x])^2)*x^4)/(2*x^2 - Log[x])^2, x] + 8*Defer[Int][(E^((x^4*(1 -
2*x^2 + 2*x^3 + Log[x] - x*Log[x])^2)/(2*x^2 - Log[x])^2)*x^5)/(2*x^2 - Log[x])^2, x] - 8*Defer[Int][(E^((x^4*
(1 - 2*x^2 + 2*x^3 + Log[x] - x*Log[x])^2)/(2*x^2 - Log[x])^2)*x^6)/(2*x^2 - Log[x])^2, x] - 8*Defer[Int][(E^(
(x^4*(1 - 2*x^2 + 2*x^3 + Log[x] - x*Log[x])^2)/(2*x^2 - Log[x])^2)*x^3)/(2*x^2 - Log[x]), x] + 10*Defer[Int][
(E^((x^4*(1 - 2*x^2 + 2*x^3 + Log[x] - x*Log[x])^2)/(2*x^2 - Log[x])^2)*x^4)/(2*x^2 - Log[x]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) \left (2 x^3-4 x^5+4 x^6-16 x^7+24 x^8+32 x^9-80 x^{10}+48 x^{11}-\left (2 x^3+2 x^4-24 x^5+32 x^6+48 x^7-120 x^8+72 x^9\right ) \log (x)-\left (8 x^3-10 x^4-24 x^5+60 x^6-36 x^7\right ) \log ^2(x)-\left (4 x^3-10 x^4+6 x^5\right ) \log ^3(x)\right )}{\left (2 x^2-\log (x)\right )^3} \, dx\\ &=\int \left (2 \exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^3 \left (2-5 x+3 x^2\right )-\frac {2 \exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^3 \left (-1+4 x^2\right )}{\left (2 x^2-\log (x)\right )^3}-\frac {2 \exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^3 \left (-1-x-4 x^2+4 x^3\right )}{\left (2 x^2-\log (x)\right )^2}+\frac {2 \exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^3 (-4+5 x)}{2 x^2-\log (x)}\right ) \, dx\\ &=2 \int \exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^3 \left (2-5 x+3 x^2\right ) \, dx-2 \int \frac {\exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^3 \left (-1+4 x^2\right )}{\left (2 x^2-\log (x)\right )^3} \, dx-2 \int \frac {\exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^3 \left (-1-x-4 x^2+4 x^3\right )}{\left (2 x^2-\log (x)\right )^2} \, dx+2 \int \frac {\exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^3 (-4+5 x)}{2 x^2-\log (x)} \, dx\\ &=2 \int \left (2 \exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^3-5 \exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^4+3 \exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^5\right ) \, dx-2 \int \left (-\frac {\exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^3}{\left (2 x^2-\log (x)\right )^3}+\frac {4 \exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^5}{\left (2 x^2-\log (x)\right )^3}\right ) \, dx-2 \int \left (-\frac {\exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^3}{\left (2 x^2-\log (x)\right )^2}-\frac {\exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^4}{\left (2 x^2-\log (x)\right )^2}-\frac {4 \exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^5}{\left (2 x^2-\log (x)\right )^2}+\frac {4 \exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^6}{\left (2 x^2-\log (x)\right )^2}\right ) \, dx+2 \int \left (-\frac {4 \exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^3}{2 x^2-\log (x)}+\frac {5 \exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^4}{2 x^2-\log (x)}\right ) \, dx\\ &=2 \int \frac {\exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^3}{\left (2 x^2-\log (x)\right )^3} \, dx+2 \int \frac {\exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^3}{\left (2 x^2-\log (x)\right )^2} \, dx+2 \int \frac {\exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^4}{\left (2 x^2-\log (x)\right )^2} \, dx+4 \int \exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^3 \, dx+6 \int \exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^5 \, dx-8 \int \frac {\exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^5}{\left (2 x^2-\log (x)\right )^3} \, dx+8 \int \frac {\exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^5}{\left (2 x^2-\log (x)\right )^2} \, dx-8 \int \frac {\exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^6}{\left (2 x^2-\log (x)\right )^2} \, dx-8 \int \frac {\exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^3}{2 x^2-\log (x)} \, dx-10 \int \exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^4 \, dx+10 \int \frac {\exp \left (\frac {x^4 \left (1-2 x^2+2 x^3+\log (x)-x \log (x)\right )^2}{\left (2 x^2-\log (x)\right )^2}\right ) x^4}{2 x^2-\log (x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.40, size = 77, normalized size = 2.20 \begin {gather*} e^{\frac {x^4 \left (\left (1-2 x^2+2 x^3\right )^2+(-1+x)^2 \log ^2(x)\right )}{\left (-2 x^2+\log (x)\right )^2}} x^{-\frac {2 x^4 \left (-1+x+2 x^2-4 x^3+2 x^4\right )}{\left (-2 x^2+\log (x)\right )^2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((x^4 - 4*x^6 + 4*x^7 + 4*x^8 - 8*x^9 + 4*x^10 + (2*x^4 - 2*x^5 - 4*x^6 + 8*x^7 - 4*x^8)*Log[x] +
(x^4 - 2*x^5 + x^6)*Log[x]^2)/(4*x^4 - 4*x^2*Log[x] + Log[x]^2))*(-2*x^3 + 4*x^5 - 4*x^6 + 16*x^7 - 24*x^8 -
32*x^9 + 80*x^10 - 48*x^11 + (2*x^3 + 2*x^4 - 24*x^5 + 32*x^6 + 48*x^7 - 120*x^8 + 72*x^9)*Log[x] + (8*x^3 - 1
0*x^4 - 24*x^5 + 60*x^6 - 36*x^7)*Log[x]^2 + (4*x^3 - 10*x^4 + 6*x^5)*Log[x]^3))/(-8*x^6 + 12*x^4*Log[x] - 6*x
^2*Log[x]^2 + Log[x]^3),x]

[Out]

E^((x^4*((1 - 2*x^2 + 2*x^3)^2 + (-1 + x)^2*Log[x]^2))/(-2*x^2 + Log[x])^2)/x^((2*x^4*(-1 + x + 2*x^2 - 4*x^3
+ 2*x^4))/(-2*x^2 + Log[x])^2)

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fricas [B]  time = 0.61, size = 95, normalized size = 2.71 \begin {gather*} e^{\left (\frac {4 \, x^{10} - 8 \, x^{9} + 4 \, x^{8} + 4 \, x^{7} - 4 \, x^{6} + x^{4} + {\left (x^{6} - 2 \, x^{5} + x^{4}\right )} \log \relax (x)^{2} - 2 \, {\left (2 \, x^{8} - 4 \, x^{7} + 2 \, x^{6} + x^{5} - x^{4}\right )} \log \relax (x)}{4 \, x^{4} - 4 \, x^{2} \log \relax (x) + \log \relax (x)^{2}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6*x^5-10*x^4+4*x^3)*log(x)^3+(-36*x^7+60*x^6-24*x^5-10*x^4+8*x^3)*log(x)^2+(72*x^9-120*x^8+48*x^7+
32*x^6-24*x^5+2*x^4+2*x^3)*log(x)-48*x^11+80*x^10-32*x^9-24*x^8+16*x^7-4*x^6+4*x^5-2*x^3)*exp(((x^6-2*x^5+x^4)
*log(x)^2+(-4*x^8+8*x^7-4*x^6-2*x^5+2*x^4)*log(x)+4*x^10-8*x^9+4*x^8+4*x^7-4*x^6+x^4)/(log(x)^2-4*x^2*log(x)+4
*x^4))/(log(x)^3-6*x^2*log(x)^2+12*x^4*log(x)-8*x^6),x, algorithm="fricas")

[Out]

e^((4*x^10 - 8*x^9 + 4*x^8 + 4*x^7 - 4*x^6 + x^4 + (x^6 - 2*x^5 + x^4)*log(x)^2 - 2*(2*x^8 - 4*x^7 + 2*x^6 + x
^5 - x^4)*log(x))/(4*x^4 - 4*x^2*log(x) + log(x)^2))

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giac [B]  time = 2.65, size = 357, normalized size = 10.20 \begin {gather*} e^{\left (\frac {4 \, x^{10}}{4 \, x^{4} - 4 \, x^{2} \log \relax (x) + \log \relax (x)^{2}} - \frac {8 \, x^{9}}{4 \, x^{4} - 4 \, x^{2} \log \relax (x) + \log \relax (x)^{2}} - \frac {4 \, x^{8} \log \relax (x)}{4 \, x^{4} - 4 \, x^{2} \log \relax (x) + \log \relax (x)^{2}} + \frac {4 \, x^{8}}{4 \, x^{4} - 4 \, x^{2} \log \relax (x) + \log \relax (x)^{2}} + \frac {8 \, x^{7} \log \relax (x)}{4 \, x^{4} - 4 \, x^{2} \log \relax (x) + \log \relax (x)^{2}} + \frac {x^{6} \log \relax (x)^{2}}{4 \, x^{4} - 4 \, x^{2} \log \relax (x) + \log \relax (x)^{2}} + \frac {4 \, x^{7}}{4 \, x^{4} - 4 \, x^{2} \log \relax (x) + \log \relax (x)^{2}} - \frac {4 \, x^{6} \log \relax (x)}{4 \, x^{4} - 4 \, x^{2} \log \relax (x) + \log \relax (x)^{2}} - \frac {2 \, x^{5} \log \relax (x)^{2}}{4 \, x^{4} - 4 \, x^{2} \log \relax (x) + \log \relax (x)^{2}} - \frac {4 \, x^{6}}{4 \, x^{4} - 4 \, x^{2} \log \relax (x) + \log \relax (x)^{2}} - \frac {2 \, x^{5} \log \relax (x)}{4 \, x^{4} - 4 \, x^{2} \log \relax (x) + \log \relax (x)^{2}} + \frac {x^{4} \log \relax (x)^{2}}{4 \, x^{4} - 4 \, x^{2} \log \relax (x) + \log \relax (x)^{2}} + \frac {2 \, x^{4} \log \relax (x)}{4 \, x^{4} - 4 \, x^{2} \log \relax (x) + \log \relax (x)^{2}} + \frac {x^{4}}{4 \, x^{4} - 4 \, x^{2} \log \relax (x) + \log \relax (x)^{2}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6*x^5-10*x^4+4*x^3)*log(x)^3+(-36*x^7+60*x^6-24*x^5-10*x^4+8*x^3)*log(x)^2+(72*x^9-120*x^8+48*x^7+
32*x^6-24*x^5+2*x^4+2*x^3)*log(x)-48*x^11+80*x^10-32*x^9-24*x^8+16*x^7-4*x^6+4*x^5-2*x^3)*exp(((x^6-2*x^5+x^4)
*log(x)^2+(-4*x^8+8*x^7-4*x^6-2*x^5+2*x^4)*log(x)+4*x^10-8*x^9+4*x^8+4*x^7-4*x^6+x^4)/(log(x)^2-4*x^2*log(x)+4
*x^4))/(log(x)^3-6*x^2*log(x)^2+12*x^4*log(x)-8*x^6),x, algorithm="giac")

[Out]

e^(4*x^10/(4*x^4 - 4*x^2*log(x) + log(x)^2) - 8*x^9/(4*x^4 - 4*x^2*log(x) + log(x)^2) - 4*x^8*log(x)/(4*x^4 -
4*x^2*log(x) + log(x)^2) + 4*x^8/(4*x^4 - 4*x^2*log(x) + log(x)^2) + 8*x^7*log(x)/(4*x^4 - 4*x^2*log(x) + log(
x)^2) + x^6*log(x)^2/(4*x^4 - 4*x^2*log(x) + log(x)^2) + 4*x^7/(4*x^4 - 4*x^2*log(x) + log(x)^2) - 4*x^6*log(x
)/(4*x^4 - 4*x^2*log(x) + log(x)^2) - 2*x^5*log(x)^2/(4*x^4 - 4*x^2*log(x) + log(x)^2) - 4*x^6/(4*x^4 - 4*x^2*
log(x) + log(x)^2) - 2*x^5*log(x)/(4*x^4 - 4*x^2*log(x) + log(x)^2) + x^4*log(x)^2/(4*x^4 - 4*x^2*log(x) + log
(x)^2) + 2*x^4*log(x)/(4*x^4 - 4*x^2*log(x) + log(x)^2) + x^4/(4*x^4 - 4*x^2*log(x) + log(x)^2))

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maple [A]  time = 0.05, size = 38, normalized size = 1.09

method	result	size
risch	\({\mathrm e}^{\frac {x^{4} \left (-2 x^{3}+x \ln \relax (x )+2 x^{2}-\ln \relax (x )-1\right )^{2}}{\left (-2 x^{2}+\ln \relax (x )\right )^{2}}}\)	\(38\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((6*x^5-10*x^4+4*x^3)*ln(x)^3+(-36*x^7+60*x^6-24*x^5-10*x^4+8*x^3)*ln(x)^2+(72*x^9-120*x^8+48*x^7+32*x^6-2
4*x^5+2*x^4+2*x^3)*ln(x)-48*x^11+80*x^10-32*x^9-24*x^8+16*x^7-4*x^6+4*x^5-2*x^3)*exp(((x^6-2*x^5+x^4)*ln(x)^2+
(-4*x^8+8*x^7-4*x^6-2*x^5+2*x^4)*ln(x)+4*x^10-8*x^9+4*x^8+4*x^7-4*x^6+x^4)/(ln(x)^2-4*x^2*ln(x)+4*x^4))/(ln(x)
^3-6*x^2*ln(x)^2+12*x^4*ln(x)-8*x^6),x,method=_RETURNVERBOSE)

[Out]

exp(x^4*(-2*x^3+x*ln(x)+2*x^2-ln(x)-1)^2/(-2*x^2+ln(x))^2)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} 2 \, \int \frac {{\left (24 \, x^{11} - 40 \, x^{10} + 16 \, x^{9} + 12 \, x^{8} - 8 \, x^{7} + 2 \, x^{6} - 2 \, x^{5} - {\left (3 \, x^{5} - 5 \, x^{4} + 2 \, x^{3}\right )} \log \relax (x)^{3} + x^{3} + {\left (18 \, x^{7} - 30 \, x^{6} + 12 \, x^{5} + 5 \, x^{4} - 4 \, x^{3}\right )} \log \relax (x)^{2} - {\left (36 \, x^{9} - 60 \, x^{8} + 24 \, x^{7} + 16 \, x^{6} - 12 \, x^{5} + x^{4} + x^{3}\right )} \log \relax (x)\right )} e^{\left (\frac {4 \, x^{10} - 8 \, x^{9} + 4 \, x^{8} + 4 \, x^{7} - 4 \, x^{6} + x^{4} + {\left (x^{6} - 2 \, x^{5} + x^{4}\right )} \log \relax (x)^{2} - 2 \, {\left (2 \, x^{8} - 4 \, x^{7} + 2 \, x^{6} + x^{5} - x^{4}\right )} \log \relax (x)}{4 \, x^{4} - 4 \, x^{2} \log \relax (x) + \log \relax (x)^{2}}\right )}}{8 \, x^{6} - 12 \, x^{4} \log \relax (x) + 6 \, x^{2} \log \relax (x)^{2} - \log \relax (x)^{3}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6*x^5-10*x^4+4*x^3)*log(x)^3+(-36*x^7+60*x^6-24*x^5-10*x^4+8*x^3)*log(x)^2+(72*x^9-120*x^8+48*x^7+
32*x^6-24*x^5+2*x^4+2*x^3)*log(x)-48*x^11+80*x^10-32*x^9-24*x^8+16*x^7-4*x^6+4*x^5-2*x^3)*exp(((x^6-2*x^5+x^4)
*log(x)^2+(-4*x^8+8*x^7-4*x^6-2*x^5+2*x^4)*log(x)+4*x^10-8*x^9+4*x^8+4*x^7-4*x^6+x^4)/(log(x)^2-4*x^2*log(x)+4
*x^4))/(log(x)^3-6*x^2*log(x)^2+12*x^4*log(x)-8*x^6),x, algorithm="maxima")

[Out]

2*integrate((24*x^11 - 40*x^10 + 16*x^9 + 12*x^8 - 8*x^7 + 2*x^6 - 2*x^5 - (3*x^5 - 5*x^4 + 2*x^3)*log(x)^3 +
x^3 + (18*x^7 - 30*x^6 + 12*x^5 + 5*x^4 - 4*x^3)*log(x)^2 - (36*x^9 - 60*x^8 + 24*x^7 + 16*x^6 - 12*x^5 + x^4
+ x^3)*log(x))*e^((4*x^10 - 8*x^9 + 4*x^8 + 4*x^7 - 4*x^6 + x^4 + (x^6 - 2*x^5 + x^4)*log(x)^2 - 2*(2*x^8 - 4*
x^7 + 2*x^6 + x^5 - x^4)*log(x))/(4*x^4 - 4*x^2*log(x) + log(x)^2))/(8*x^6 - 12*x^4*log(x) + 6*x^2*log(x)^2 -
log(x)^3), x)

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mupad [B]  time = 5.83, size = 284, normalized size = 8.11 \begin {gather*} \frac {{\mathrm {e}}^{\frac {x^4\,{\ln \relax (x)}^2}{4\,x^4-4\,x^2\,\ln \relax (x)+{\ln \relax (x)}^2}}\,{\mathrm {e}}^{\frac {x^6\,{\ln \relax (x)}^2}{4\,x^4-4\,x^2\,\ln \relax (x)+{\ln \relax (x)}^2}}\,{\mathrm {e}}^{-\frac {2\,x^5\,{\ln \relax (x)}^2}{4\,x^4-4\,x^2\,\ln \relax (x)+{\ln \relax (x)}^2}}\,{\mathrm {e}}^{\frac {x^4}{4\,x^4-4\,x^2\,\ln \relax (x)+{\ln \relax (x)}^2}}\,{\mathrm {e}}^{-\frac {4\,x^6}{4\,x^4-4\,x^2\,\ln \relax (x)+{\ln \relax (x)}^2}}\,{\mathrm {e}}^{\frac {4\,x^7}{4\,x^4-4\,x^2\,\ln \relax (x)+{\ln \relax (x)}^2}}\,{\mathrm {e}}^{\frac {4\,x^8}{4\,x^4-4\,x^2\,\ln \relax (x)+{\ln \relax (x)}^2}}\,{\mathrm {e}}^{\frac {4\,x^{10}}{4\,x^4-4\,x^2\,\ln \relax (x)+{\ln \relax (x)}^2}}\,{\mathrm {e}}^{-\frac {8\,x^9}{4\,x^4-4\,x^2\,\ln \relax (x)+{\ln \relax (x)}^2}}}{x^{\frac {2\,\left (2\,x^8-4\,x^7+2\,x^6+x^5-x^4\right )}{4\,x^4-4\,x^2\,\ln \relax (x)+{\ln \relax (x)}^2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp((x^4 - log(x)*(2*x^5 - 2*x^4 + 4*x^6 - 8*x^7 + 4*x^8) - 4*x^6 + 4*x^7 + 4*x^8 - 8*x^9 + 4*x^10 + log
(x)^2*(x^4 - 2*x^5 + x^6))/(log(x)^2 - 4*x^2*log(x) + 4*x^4))*(log(x)^2*(10*x^4 - 8*x^3 + 24*x^5 - 60*x^6 + 36
*x^7) - log(x)*(2*x^3 + 2*x^4 - 24*x^5 + 32*x^6 + 48*x^7 - 120*x^8 + 72*x^9) - log(x)^3*(4*x^3 - 10*x^4 + 6*x^
5) + 2*x^3 - 4*x^5 + 4*x^6 - 16*x^7 + 24*x^8 + 32*x^9 - 80*x^10 + 48*x^11))/(12*x^4*log(x) + log(x)^3 - 6*x^2*
log(x)^2 - 8*x^6),x)

[Out]

(exp((x^4*log(x)^2)/(log(x)^2 - 4*x^2*log(x) + 4*x^4))*exp((x^6*log(x)^2)/(log(x)^2 - 4*x^2*log(x) + 4*x^4))*e
xp(-(2*x^5*log(x)^2)/(log(x)^2 - 4*x^2*log(x) + 4*x^4))*exp(x^4/(log(x)^2 - 4*x^2*log(x) + 4*x^4))*exp(-(4*x^6
)/(log(x)^2 - 4*x^2*log(x) + 4*x^4))*exp((4*x^7)/(log(x)^2 - 4*x^2*log(x) + 4*x^4))*exp((4*x^8)/(log(x)^2 - 4*
x^2*log(x) + 4*x^4))*exp((4*x^10)/(log(x)^2 - 4*x^2*log(x) + 4*x^4))*exp(-(8*x^9)/(log(x)^2 - 4*x^2*log(x) + 4
*x^4)))/x^((2*(x^5 - x^4 + 2*x^6 - 4*x^7 + 2*x^8))/(log(x)^2 - 4*x^2*log(x) + 4*x^4))

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sympy [B]  time = 1.76, size = 94, normalized size = 2.69 \begin {gather*} e^{\frac {4 x^{10} - 8 x^{9} + 4 x^{8} + 4 x^{7} - 4 x^{6} + x^{4} + \left (x^{6} - 2 x^{5} + x^{4}\right ) \log {\relax (x )}^{2} + \left (- 4 x^{8} + 8 x^{7} - 4 x^{6} - 2 x^{5} + 2 x^{4}\right ) \log {\relax (x )}}{4 x^{4} - 4 x^{2} \log {\relax (x )} + \log {\relax (x )}^{2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((6*x**5-10*x**4+4*x**3)*ln(x)**3+(-36*x**7+60*x**6-24*x**5-10*x**4+8*x**3)*ln(x)**2+(72*x**9-120*x*
*8+48*x**7+32*x**6-24*x**5+2*x**4+2*x**3)*ln(x)-48*x**11+80*x**10-32*x**9-24*x**8+16*x**7-4*x**6+4*x**5-2*x**3
)*exp(((x**6-2*x**5+x**4)*ln(x)**2+(-4*x**8+8*x**7-4*x**6-2*x**5+2*x**4)*ln(x)+4*x**10-8*x**9+4*x**8+4*x**7-4*
x**6+x**4)/(ln(x)**2-4*x**2*ln(x)+4*x**4))/(ln(x)**3-6*x**2*ln(x)**2+12*x**4*ln(x)-8*x**6),x)

[Out]

exp((4*x**10 - 8*x**9 + 4*x**8 + 4*x**7 - 4*x**6 + x**4 + (x**6 - 2*x**5 + x**4)*log(x)**2 + (-4*x**8 + 8*x**7
- 4*x**6 - 2*x**5 + 2*x**4)*log(x))/(4*x**4 - 4*x**2*log(x) + log(x)**2))

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