3.31.73 \(\int \frac {64 e^{-36+16 x-2 x^2} (-\frac {1}{64} e^{36-16 x+2 x^2} x^3 \log ^3(x)+e^{\frac {64 e^{-36+16 x-2 x^2} (16-4 e^{18-8 x+x^2} x+\frac {1}{4} e^{36-16 x+2 x^2} x^2)}{x^2 \log ^2(x)}} (-32-\frac {1}{2} e^{36-16 x+2 x^2} x^2+(-32+256 x-64 x^2) \log (x)+\frac {1}{8} e^{18-8 x+x^2} x (64+(32-256 x+64 x^2) \log (x))))}{x^3 \log ^3(x)} \, dx\)

Optimal. Leaf size=31 \[ e^{\frac {\left (-4+\frac {32 e^{-2-(-4+x)^2}}{x}\right )^2}{\log ^2(x)}}-x \]

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Rubi [F]  time = 41.38, 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 {64 e^{-36+16 x-2 x^2} \left (-\frac {1}{64} e^{36-16 x+2 x^2} x^3 \log ^3(x)+\exp \left (\frac {64 e^{-36+16 x-2 x^2} \left (16-4 e^{18-8 x+x^2} x+\frac {1}{4} e^{36-16 x+2 x^2} x^2\right )}{x^2 \log ^2(x)}\right ) \left (-32-\frac {1}{2} e^{36-16 x+2 x^2} x^2+\left (-32+256 x-64 x^2\right ) \log (x)+\frac {1}{8} e^{18-8 x+x^2} x \left (64+\left (32-256 x+64 x^2\right ) \log (x)\right )\right )\right )}{x^3 \log ^3(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(64*E^(-36 + 16*x - 2*x^2)*(-1/64*(E^(36 - 16*x + 2*x^2)*x^3*Log[x]^3) + E^((64*E^(-36 + 16*x - 2*x^2)*(16
- 4*E^(18 - 8*x + x^2)*x + (E^(36 - 16*x + 2*x^2)*x^2)/4))/(x^2*Log[x]^2))*(-32 - (E^(36 - 16*x + 2*x^2)*x^2)
/2 + (-32 + 256*x - 64*x^2)*Log[x] + (E^(18 - 8*x + x^2)*x*(64 + (32 - 256*x + 64*x^2)*Log[x]))/8)))/(x^3*Log[
x]^3),x]

[Out]

-x - 2048*Defer[Int][E^(16*x - 2*(18 + x^2 - (8*(-8*E^(8*x) + E^(18 + x^2)*x)^2)/(E^(2*(18 + x^2))*x^2*Log[x]^
2)))/(x^3*Log[x]^3), x] + 512*Defer[Int][E^(18 + 8*x + x^2 - 2*(18 + x^2 - (8*(-8*E^(8*x) + E^(18 + x^2)*x)^2)
/(E^(2*(18 + x^2))*x^2*Log[x]^2)))/(x^2*Log[x]^3), x] - 32*Defer[Int][E^((16*E^(-36 - 2*x^2)*(-8*E^(8*x) + E^(
18 + x^2)*x)^2)/(x^2*Log[x]^2))/(x*Log[x]^3), x] + 512*Defer[Int][E^(18 + 8*x + x^2 - 2*(18 + x^2 - (8*(-8*E^(
8*x) + E^(18 + x^2)*x)^2)/(E^(2*(18 + x^2))*x^2*Log[x]^2)))/Log[x]^2, x] - 2048*Defer[Int][E^(16*x - 2*(18 + x
^2 - (8*(-8*E^(8*x) + E^(18 + x^2)*x)^2)/(E^(2*(18 + x^2))*x^2*Log[x]^2)))/(x^3*Log[x]^2), x] + 16384*Defer[In
t][E^(16*x - 2*(18 + x^2 - (8*(-8*E^(8*x) + E^(18 + x^2)*x)^2)/(E^(2*(18 + x^2))*x^2*Log[x]^2)))/(x^2*Log[x]^2
), x] + 256*Defer[Int][E^(18 + 8*x + x^2 - 2*(18 + x^2 - (8*(-8*E^(8*x) + E^(18 + x^2)*x)^2)/(E^(2*(18 + x^2))
*x^2*Log[x]^2)))/(x^2*Log[x]^2), x] - 4096*Defer[Int][E^(16*x - 2*(18 + x^2 - (8*(-8*E^(8*x) + E^(18 + x^2)*x)
^2)/(E^(2*(18 + x^2))*x^2*Log[x]^2)))/(x*Log[x]^2), x] - 2048*Defer[Int][E^(18 + 8*x + x^2 - 2*(18 + x^2 - (8*
(-8*E^(8*x) + E^(18 + x^2)*x)^2)/(E^(2*(18 + x^2))*x^2*Log[x]^2)))/(x*Log[x]^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=64 \int \frac {e^{-36+16 x-2 x^2} \left (-\frac {1}{64} e^{36-16 x+2 x^2} x^3 \log ^3(x)+\exp \left (\frac {64 e^{-36+16 x-2 x^2} \left (16-4 e^{18-8 x+x^2} x+\frac {1}{4} e^{36-16 x+2 x^2} x^2\right )}{x^2 \log ^2(x)}\right ) \left (-32-\frac {1}{2} e^{36-16 x+2 x^2} x^2+\left (-32+256 x-64 x^2\right ) \log (x)+\frac {1}{8} e^{18-8 x+x^2} x \left (64+\left (32-256 x+64 x^2\right ) \log (x)\right )\right )\right )}{x^3 \log ^3(x)} \, dx\\ &=64 \int \left (-\frac {1}{64}-\frac {\exp \left (-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right ) \left (-8 e^{8 x}+e^{18+x^2} x\right ) \left (-8 e^{8 x}+e^{18+x^2} x-8 e^{8 x} \left (1-8 x+2 x^2\right ) \log (x)\right )}{2 x^3 \log ^3(x)}\right ) \, dx\\ &=-x-32 \int \frac {\exp \left (-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right ) \left (-8 e^{8 x}+e^{18+x^2} x\right ) \left (-8 e^{8 x}+e^{18+x^2} x-8 e^{8 x} \left (1-8 x+2 x^2\right ) \log (x)\right )}{x^3 \log ^3(x)} \, dx\\ &=-x-32 \int \left (\frac {\exp \left (36+2 x^2-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{x \log ^3(x)}+\frac {64 \exp \left (16 x-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right ) \left (1+\log (x)-8 x \log (x)+2 x^2 \log (x)\right )}{x^3 \log ^3(x)}-\frac {8 \exp \left (18+8 x+x^2-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right ) \left (2+\log (x)-8 x \log (x)+2 x^2 \log (x)\right )}{x^2 \log ^3(x)}\right ) \, dx\\ &=-x-32 \int \frac {\exp \left (36+2 x^2-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{x \log ^3(x)} \, dx+256 \int \frac {\exp \left (18+8 x+x^2-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right ) \left (2+\log (x)-8 x \log (x)+2 x^2 \log (x)\right )}{x^2 \log ^3(x)} \, dx-2048 \int \frac {\exp \left (16 x-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right ) \left (1+\log (x)-8 x \log (x)+2 x^2 \log (x)\right )}{x^3 \log ^3(x)} \, dx\\ &=-x-32 \int \frac {\exp \left (\frac {16 e^{-36-2 x^2} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )}{x \log ^3(x)} \, dx+256 \int \left (\frac {2 \exp \left (18+8 x+x^2-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{x^2 \log ^3(x)}+\frac {\exp \left (18+8 x+x^2-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right ) \left (1-8 x+2 x^2\right )}{x^2 \log ^2(x)}\right ) \, dx-2048 \int \left (\frac {\exp \left (16 x-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{x^3 \log ^3(x)}+\frac {\exp \left (16 x-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right ) \left (1-8 x+2 x^2\right )}{x^3 \log ^2(x)}\right ) \, dx\\ &=-x-32 \int \frac {\exp \left (\frac {16 e^{-36-2 x^2} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )}{x \log ^3(x)} \, dx+256 \int \frac {\exp \left (18+8 x+x^2-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right ) \left (1-8 x+2 x^2\right )}{x^2 \log ^2(x)} \, dx+512 \int \frac {\exp \left (18+8 x+x^2-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{x^2 \log ^3(x)} \, dx-2048 \int \frac {\exp \left (16 x-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{x^3 \log ^3(x)} \, dx-2048 \int \frac {\exp \left (16 x-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right ) \left (1-8 x+2 x^2\right )}{x^3 \log ^2(x)} \, dx\\ &=-x-32 \int \frac {\exp \left (\frac {16 e^{-36-2 x^2} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )}{x \log ^3(x)} \, dx+256 \int \left (\frac {2 \exp \left (18+8 x+x^2-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{\log ^2(x)}+\frac {\exp \left (18+8 x+x^2-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{x^2 \log ^2(x)}-\frac {8 \exp \left (18+8 x+x^2-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{x \log ^2(x)}\right ) \, dx+512 \int \frac {\exp \left (18+8 x+x^2-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{x^2 \log ^3(x)} \, dx-2048 \int \left (\frac {\exp \left (16 x-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{x^3 \log ^2(x)}-\frac {8 \exp \left (16 x-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{x^2 \log ^2(x)}+\frac {2 \exp \left (16 x-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{x \log ^2(x)}\right ) \, dx-2048 \int \frac {\exp \left (16 x-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{x^3 \log ^3(x)} \, dx\\ &=-x-32 \int \frac {\exp \left (\frac {16 e^{-36-2 x^2} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )}{x \log ^3(x)} \, dx+256 \int \frac {\exp \left (18+8 x+x^2-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{x^2 \log ^2(x)} \, dx+512 \int \frac {\exp \left (18+8 x+x^2-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{x^2 \log ^3(x)} \, dx+512 \int \frac {\exp \left (18+8 x+x^2-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{\log ^2(x)} \, dx-2048 \int \frac {\exp \left (16 x-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{x^3 \log ^3(x)} \, dx-2048 \int \frac {\exp \left (16 x-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{x^3 \log ^2(x)} \, dx-2048 \int \frac {\exp \left (18+8 x+x^2-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{x \log ^2(x)} \, dx-4096 \int \frac {\exp \left (16 x-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{x \log ^2(x)} \, dx+16384 \int \frac {\exp \left (16 x-2 \left (18+x^2-\frac {8 e^{-2 \left (18+x^2\right )} \left (-8 e^{8 x}+e^{18+x^2} x\right )^2}{x^2 \log ^2(x)}\right )\right )}{x^2 \log ^2(x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.34, size = 39, normalized size = 1.26 \begin {gather*} e^{\frac {16 \left (-8 e^{8 x-x^2}+e^{18} x\right )^2}{e^{36} x^2 \log ^2(x)}}-x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(64*E^(-36 + 16*x - 2*x^2)*(-1/64*(E^(36 - 16*x + 2*x^2)*x^3*Log[x]^3) + E^((64*E^(-36 + 16*x - 2*x^
2)*(16 - 4*E^(18 - 8*x + x^2)*x + (E^(36 - 16*x + 2*x^2)*x^2)/4))/(x^2*Log[x]^2))*(-32 - (E^(36 - 16*x + 2*x^2
)*x^2)/2 + (-32 + 256*x - 64*x^2)*Log[x] + (E^(18 - 8*x + x^2)*x*(64 + (32 - 256*x + 64*x^2)*Log[x]))/8)))/(x^
3*Log[x]^3),x]

[Out]

E^((16*(-8*E^(8*x - x^2) + E^18*x)^2)/(E^36*x^2*Log[x]^2)) - x

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fricas [B]  time = 0.71, size = 81, normalized size = 2.61 \begin {gather*} -x + e^{\left (\frac {16 \, {\left (e^{\left (2 \, x^{2} - 16 \, x + 2 \, \log \left (\frac {1}{8} \, x\right ) + 36\right )} - 2 \, e^{\left (x^{2} - 8 \, x + \log \left (\frac {1}{8} \, x\right ) + 18\right )} + 1\right )} e^{\left (-2 \, x^{2} + 16 \, x - 2 \, \log \left (\frac {1}{8} \, x\right ) - 36\right )}}{9 \, \log \relax (2)^{2} + 6 \, \log \relax (2) \log \left (\frac {1}{8} \, x\right ) + \log \left (\frac {1}{8} \, x\right )^{2}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-32*exp(log(1/8*x)+x^2-8*x+18)^2+((64*x^2-256*x+32)*log(x)+64)*exp(log(1/8*x)+x^2-8*x+18)+(-64*x^2
+256*x-32)*log(x)-32)*exp((16*exp(log(1/8*x)+x^2-8*x+18)^2-32*exp(log(1/8*x)+x^2-8*x+18)+16)/log(x)^2/exp(log(
1/8*x)+x^2-8*x+18)^2)-x*log(x)^3*exp(log(1/8*x)+x^2-8*x+18)^2)/x/log(x)^3/exp(log(1/8*x)+x^2-8*x+18)^2,x, algo
rithm="fricas")

[Out]

-x + e^(16*(e^(2*x^2 - 16*x + 2*log(1/8*x) + 36) - 2*e^(x^2 - 8*x + log(1/8*x) + 18) + 1)*e^(-2*x^2 + 16*x - 2
*log(1/8*x) - 36)/(9*log(2)^2 + 6*log(2)*log(1/8*x) + log(1/8*x)^2))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \mathit {undef} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-32*exp(log(1/8*x)+x^2-8*x+18)^2+((64*x^2-256*x+32)*log(x)+64)*exp(log(1/8*x)+x^2-8*x+18)+(-64*x^2
+256*x-32)*log(x)-32)*exp((16*exp(log(1/8*x)+x^2-8*x+18)^2-32*exp(log(1/8*x)+x^2-8*x+18)+16)/log(x)^2/exp(log(
1/8*x)+x^2-8*x+18)^2)-x*log(x)^3*exp(log(1/8*x)+x^2-8*x+18)^2)/x/log(x)^3/exp(log(1/8*x)+x^2-8*x+18)^2,x, algo
rithm="giac")

[Out]

undef

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maple [A]  time = 0.15, size = 55, normalized size = 1.77

method	result	size
risch	\(-x +{\mathrm e}^{\frac {16 \left (x^{2} {\mathrm e}^{2 x^{2}-16 x +36}-16 x \,{\mathrm e}^{x^{2}-8 x +18}+64\right ) {\mathrm e}^{-2 x^{2}+16 x -36}}{\ln \relax (x )^{2} x^{2}}}\)	\(55\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-32*exp(ln(1/8*x)+x^2-8*x+18)^2+((64*x^2-256*x+32)*ln(x)+64)*exp(ln(1/8*x)+x^2-8*x+18)+(-64*x^2+256*x-32
)*ln(x)-32)*exp((16*exp(ln(1/8*x)+x^2-8*x+18)^2-32*exp(ln(1/8*x)+x^2-8*x+18)+16)/ln(x)^2/exp(ln(1/8*x)+x^2-8*x
+18)^2)-x*ln(x)^3*exp(ln(1/8*x)+x^2-8*x+18)^2)/x/ln(x)^3/exp(ln(1/8*x)+x^2-8*x+18)^2,x,method=_RETURNVERBOSE)

[Out]

-x+exp(16*(x^2*exp(2*x^2-16*x+36)-16*x*exp(x^2-8*x+18)+64)*exp(-2*x^2+16*x-36)/ln(x)^2/x^2)

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maxima [A]  time = 0.79, size = 52, normalized size = 1.68 \begin {gather*} -x + e^{\left (-\frac {256 \, e^{\left (-x^{2} + 8 \, x - 18\right )}}{x \log \relax (x)^{2}} + \frac {16}{\log \relax (x)^{2}} + \frac {1024 \, e^{\left (-2 \, x^{2} + 16 \, x - 36\right )}}{x^{2} \log \relax (x)^{2}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-32*exp(log(1/8*x)+x^2-8*x+18)^2+((64*x^2-256*x+32)*log(x)+64)*exp(log(1/8*x)+x^2-8*x+18)+(-64*x^2
+256*x-32)*log(x)-32)*exp((16*exp(log(1/8*x)+x^2-8*x+18)^2-32*exp(log(1/8*x)+x^2-8*x+18)+16)/log(x)^2/exp(log(
1/8*x)+x^2-8*x+18)^2)-x*log(x)^3*exp(log(1/8*x)+x^2-8*x+18)^2)/x/log(x)^3/exp(log(1/8*x)+x^2-8*x+18)^2,x, algo
rithm="maxima")

[Out]

-x + e^(-256*e^(-x^2 + 8*x - 18)/(x*log(x)^2) + 16/log(x)^2 + 1024*e^(-2*x^2 + 16*x - 36)/(x^2*log(x)^2))

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mupad [B]  time = 2.04, size = 56, normalized size = 1.81 \begin {gather*} {\mathrm {e}}^{\frac {16}{{\ln \relax (x)}^2}}\,{\mathrm {e}}^{-\frac {256\,{\mathrm {e}}^{8\,x}\,{\mathrm {e}}^{-18}\,{\mathrm {e}}^{-x^2}}{x\,{\ln \relax (x)}^2}}\,{\mathrm {e}}^{\frac {1024\,{\mathrm {e}}^{16\,x}\,{\mathrm {e}}^{-36}\,{\mathrm {e}}^{-2\,x^2}}{x^2\,{\ln \relax (x)}^2}}-x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(16*x - 2*log(x/8) - 2*x^2 - 36)*(exp((exp(16*x - 2*log(x/8) - 2*x^2 - 36)*(16*exp(2*log(x/8) - 16*x
+ 2*x^2 + 36) - 32*exp(log(x/8) - 8*x + x^2 + 18) + 16))/log(x)^2)*(32*exp(2*log(x/8) - 16*x + 2*x^2 + 36) - e
xp(log(x/8) - 8*x + x^2 + 18)*(log(x)*(64*x^2 - 256*x + 32) + 64) + log(x)*(64*x^2 - 256*x + 32) + 32) + x*exp
(2*log(x/8) - 16*x + 2*x^2 + 36)*log(x)^3))/(x*log(x)^3),x)

[Out]

exp(16/log(x)^2)*exp(-(256*exp(8*x)*exp(-18)*exp(-x^2))/(x*log(x)^2))*exp((1024*exp(16*x)*exp(-36)*exp(-2*x^2)
)/(x^2*log(x)^2)) - x

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sympy [B]  time = 1.30, size = 56, normalized size = 1.81 \begin {gather*} - x + e^{\frac {64 \left (\frac {x^{2} e^{2 x^{2} - 16 x + 36}}{4} - 4 x e^{x^{2} - 8 x + 18} + 16\right ) e^{- 2 x^{2} + 16 x - 36}}{x^{2} \log {\relax (x )}^{2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-32*exp(ln(1/8*x)+x**2-8*x+18)**2+((64*x**2-256*x+32)*ln(x)+64)*exp(ln(1/8*x)+x**2-8*x+18)+(-64*x*
*2+256*x-32)*ln(x)-32)*exp((16*exp(ln(1/8*x)+x**2-8*x+18)**2-32*exp(ln(1/8*x)+x**2-8*x+18)+16)/ln(x)**2/exp(ln
(1/8*x)+x**2-8*x+18)**2)-x*ln(x)**3*exp(ln(1/8*x)+x**2-8*x+18)**2)/x/ln(x)**3/exp(ln(1/8*x)+x**2-8*x+18)**2,x)

[Out]

-x + exp(64*(x**2*exp(2*x**2 - 16*x + 36)/4 - 4*x*exp(x**2 - 8*x + 18) + 16)*exp(-2*x**2 + 16*x - 36)/(x**2*lo
g(x)**2))

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