3.46.5 \(\int \frac {e^x (1+e^4 (32-16 x)+(1+e^4 (16-16 x)) \log (3))+e^x (-1+e^4 (-16+16 x)) \log (-\frac {400}{-1+e^4 (-16+16 x)})}{-1+e^4 (-16+16 x)+(-2+e^4 (-32+32 x)) \log (3)+(-1+e^4 (-16+16 x)) \log ^2(3)+(2+e^4 (32-32 x)+(2+e^4 (32-32 x)) \log (3)) \log (-\frac {400}{-1+e^4 (-16+16 x)})+(-1+e^4 (-16+16 x)) \log ^2(-\frac {400}{-1+e^4 (-16+16 x)})} \, dx\)

Optimal. Leaf size=29 \[ \frac {e^x}{-1-\log (3)+\log \left (\frac {25}{\frac {1}{16}-e^4 (-1+x)}\right )} \]

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Rubi [F]  time = 8.03, 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 {e^x \left (1+e^4 (32-16 x)+\left (1+e^4 (16-16 x)\right ) \log (3)\right )+e^x \left (-1+e^4 (-16+16 x)\right ) \log \left (-\frac {400}{-1+e^4 (-16+16 x)}\right )}{-1+e^4 (-16+16 x)+\left (-2+e^4 (-32+32 x)\right ) \log (3)+\left (-1+e^4 (-16+16 x)\right ) \log ^2(3)+\left (2+e^4 (32-32 x)+\left (2+e^4 (32-32 x)\right ) \log (3)\right ) \log \left (-\frac {400}{-1+e^4 (-16+16 x)}\right )+\left (-1+e^4 (-16+16 x)\right ) \log ^2\left (-\frac {400}{-1+e^4 (-16+16 x)}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^x*(1 + E^4*(32 - 16*x) + (1 + E^4*(16 - 16*x))*Log[3]) + E^x*(-1 + E^4*(-16 + 16*x))*Log[-400/(-1 + E^4
*(-16 + 16*x))])/(-1 + E^4*(-16 + 16*x) + (-2 + E^4*(-32 + 32*x))*Log[3] + (-1 + E^4*(-16 + 16*x))*Log[3]^2 +
(2 + E^4*(32 - 32*x) + (2 + E^4*(32 - 32*x))*Log[3])*Log[-400/(-1 + E^4*(-16 + 16*x))] + (-1 + E^4*(-16 + 16*x
))*Log[-400/(-1 + E^4*(-16 + 16*x))]^2),x]

[Out]

-((1 + 16*E^4)*(1 + Log[3])*Defer[Int][E^x/((-1 - 16*E^4 + 16*E^4*x)*(1 + Log[3] - Log[-400/(-1 - 16*E^4 + 16*
E^4*x)])^2), x]) + (1 + Log[3] + 16*E^4*(2 + Log[3]))*Defer[Int][E^x/((-1 - 16*E^4 + 16*E^4*x)*(1 + Log[3] - L
og[-400/(-1 - 16*E^4 + 16*E^4*x)])^2), x] - Defer[Int][E^x/(1 + Log[3] - Log[-400/(-1 - 16*E^4 + 16*E^4*x)]),
x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^x \left (-1-\log (3)+16 e^4 (-2+x-\log (3)+x \log (3))-\left (-1+16 e^4 (-1+x)\right ) \log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )}{\left (1+16 e^4-16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )^2} \, dx\\ &=\int \frac {e^x \left (-1-\log (3)+16 e^4 (-2+x-\log (3)+x \log (3))-\left (-1+16 e^4 (-1+x)\right ) \log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )}{\left (1+16 e^4-16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )^2} \, dx\\ &=\int \left (-\frac {16 e^{4+x} x (1+\log (3))}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )^2}+\frac {e^x \left (1+\log (3)+16 e^4 (2+\log (3))\right )}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )^2}+\frac {e^x \left (1+16 e^4\right ) \log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )}{\left (1+16 e^4-16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )^2}+\frac {16 e^{4+x} x \log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )^2}\right ) \, dx\\ &=16 \int \frac {e^{4+x} x \log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )^2} \, dx+\left (1+16 e^4\right ) \int \frac {e^x \log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )}{\left (1+16 e^4-16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )^2} \, dx-(16 (1+\log (3))) \int \frac {e^{4+x} x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )^2} \, dx+\left (1+\log (3)+16 e^4 (2+\log (3))\right ) \int \frac {e^x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )^2} \, dx\\ &=16 \int \frac {e^{4+x} x \log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )^2} \, dx+\left (1+16 e^4\right ) \int \frac {e^x \log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )}{\left (1+16 e^4-16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )^2} \, dx-(16 (1+\log (3))) \int \frac {e^{4+x} x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )^2} \, dx+\left (1+\log (3)+16 e^4 (2+\log (3))\right ) \int \frac {e^x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )^2} \, dx\\ &=16 \int \left (\frac {e^{4+x} x (1+\log (3))}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )^2}-\frac {e^{4+x} x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )}\right ) \, dx+\left (1+16 e^4\right ) \int \left (\frac {e^x (-1-\log (3))}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )^2}+\frac {e^x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )}\right ) \, dx-(16 (1+\log (3))) \int \left (\frac {e^x}{16 \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )^2}+\frac {e^x \left (1+16 e^4\right )}{16 \left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )^2}\right ) \, dx+\left (1+\log (3)+16 e^4 (2+\log (3))\right ) \int \frac {e^x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )^2} \, dx\\ &=-\left (16 \int \frac {e^{4+x} x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )} \, dx\right )+\left (1+16 e^4\right ) \int \frac {e^x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )} \, dx-(1+\log (3)) \int \frac {e^x}{\left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )^2} \, dx+(16 (1+\log (3))) \int \frac {e^{4+x} x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )^2} \, dx-2 \left (\left (\left (1+16 e^4\right ) (1+\log (3))\right ) \int \frac {e^x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )^2} \, dx\right )+\left (1+\log (3)+16 e^4 (2+\log (3))\right ) \int \frac {e^x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )^2} \, dx\\ &=-\left (16 \int \frac {e^{4+x} x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )} \, dx\right )+\left (1+16 e^4\right ) \int \frac {e^x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )} \, dx-(1+\log (3)) \int \frac {e^x}{\left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )^2} \, dx+(16 (1+\log (3))) \int \frac {e^{4+x} x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )^2} \, dx-2 \left (\left (\left (1+16 e^4\right ) (1+\log (3))\right ) \int \frac {e^x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )^2} \, dx\right )+\left (1+\log (3)+16 e^4 (2+\log (3))\right ) \int \frac {e^x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )^2} \, dx\\ &=-\left (16 \int \left (\frac {e^x}{16 \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )}+\frac {e^x \left (1+16 e^4\right )}{16 \left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )}\right ) \, dx\right )+\left (1+16 e^4\right ) \int \frac {e^x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )} \, dx-(1+\log (3)) \int \frac {e^x}{\left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )^2} \, dx+(16 (1+\log (3))) \int \left (\frac {e^x}{16 \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )^2}+\frac {e^x \left (1+16 e^4\right )}{16 \left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )^2}\right ) \, dx-2 \left (\left (\left (1+16 e^4\right ) (1+\log (3))\right ) \int \frac {e^x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )^2} \, dx\right )+\left (1+\log (3)+16 e^4 (2+\log (3))\right ) \int \frac {e^x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )^2} \, dx\\ &=-\left (\left (1+16 e^4\right ) \int \frac {e^x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )} \, dx\right )+\left (1+16 e^4\right ) \int \frac {e^x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )} \, dx+(1+\log (3)) \int \frac {e^x}{\left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )^2} \, dx-(1+\log (3)) \int \frac {e^x}{\left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )^2} \, dx+\left (\left (1+16 e^4\right ) (1+\log (3))\right ) \int \frac {e^x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )\right )^2} \, dx-2 \left (\left (\left (1+16 e^4\right ) (1+\log (3))\right ) \int \frac {e^x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )^2} \, dx\right )+\left (1+\log (3)+16 e^4 (2+\log (3))\right ) \int \frac {e^x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )^2} \, dx-\int \frac {e^x}{1+\log (3)-\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )} \, dx\\ &=-\left (\left (\left (1+16 e^4\right ) (1+\log (3))\right ) \int \frac {e^x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )^2} \, dx\right )+\left (1+\log (3)+16 e^4 (2+\log (3))\right ) \int \frac {e^x}{\left (-1-16 e^4+16 e^4 x\right ) \left (1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )\right )^2} \, dx-\int \frac {e^x}{1+\log (3)-\log \left (-\frac {400}{-1-16 e^4+16 e^4 x}\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.09, size = 27, normalized size = 0.93 \begin {gather*} \frac {e^x}{-1-\log (3)+\log \left (-\frac {400}{-1+16 e^4 (-1+x)}\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^x*(1 + E^4*(32 - 16*x) + (1 + E^4*(16 - 16*x))*Log[3]) + E^x*(-1 + E^4*(-16 + 16*x))*Log[-400/(-1
+ E^4*(-16 + 16*x))])/(-1 + E^4*(-16 + 16*x) + (-2 + E^4*(-32 + 32*x))*Log[3] + (-1 + E^4*(-16 + 16*x))*Log[3
]^2 + (2 + E^4*(32 - 32*x) + (2 + E^4*(32 - 32*x))*Log[3])*Log[-400/(-1 + E^4*(-16 + 16*x))] + (-1 + E^4*(-16
+ 16*x))*Log[-400/(-1 + E^4*(-16 + 16*x))]^2),x]

[Out]

E^x/(-1 - Log[3] + Log[-400/(-1 + 16*E^4*(-1 + x))])

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fricas [A]  time = 0.60, size = 26, normalized size = 0.90 \begin {gather*} -\frac {e^{x}}{\log \relax (3) - \log \left (-\frac {400}{16 \, {\left (x - 1\right )} e^{4} - 1}\right ) + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((16*x-16)*exp(4)-1)*exp(x)*log(-400/((16*x-16)*exp(4)-1))+(((-16*x+16)*exp(4)+1)*log(3)+(-16*x+32)
*exp(4)+1)*exp(x))/(((16*x-16)*exp(4)-1)*log(-400/((16*x-16)*exp(4)-1))^2+(((-32*x+32)*exp(4)+2)*log(3)+(-32*x
+32)*exp(4)+2)*log(-400/((16*x-16)*exp(4)-1))+((16*x-16)*exp(4)-1)*log(3)^2+((32*x-32)*exp(4)-2)*log(3)+(16*x-
16)*exp(4)-1),x, algorithm="fricas")

[Out]

-e^x/(log(3) - log(-400/(16*(x - 1)*e^4 - 1)) + 1)

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giac [B]  time = 0.33, size = 150, normalized size = 5.17 \begin {gather*} \frac {2 \, {\left (e^{x} \log \left (400\right ) - e^{x} \log \relax (3) - e^{x} \log \left ({\left | 16 \, x e^{4} - 16 \, e^{4} - 1 \right |}\right ) - e^{x}\right )}}{\pi ^{2} \mathrm {sgn}\left (16 \, x e^{4} - 16 \, e^{4} - 1\right ) + \pi ^{2} + 2 \, \log \left (400\right )^{2} - 4 \, \log \left (400\right ) \log \relax (3) + 2 \, \log \relax (3)^{2} - 4 \, \log \left (400\right ) \log \left ({\left | 16 \, x e^{4} - 16 \, e^{4} - 1 \right |}\right ) + 4 \, \log \relax (3) \log \left ({\left | 16 \, x e^{4} - 16 \, e^{4} - 1 \right |}\right ) + 2 \, \log \left ({\left | 16 \, x e^{4} - 16 \, e^{4} - 1 \right |}\right )^{2} - 4 \, \log \left (400\right ) + 4 \, \log \relax (3) + 4 \, \log \left ({\left | 16 \, x e^{4} - 16 \, e^{4} - 1 \right |}\right ) + 2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((16*x-16)*exp(4)-1)*exp(x)*log(-400/((16*x-16)*exp(4)-1))+(((-16*x+16)*exp(4)+1)*log(3)+(-16*x+32)
*exp(4)+1)*exp(x))/(((16*x-16)*exp(4)-1)*log(-400/((16*x-16)*exp(4)-1))^2+(((-32*x+32)*exp(4)+2)*log(3)+(-32*x
+32)*exp(4)+2)*log(-400/((16*x-16)*exp(4)-1))+((16*x-16)*exp(4)-1)*log(3)^2+((32*x-32)*exp(4)-2)*log(3)+(16*x-
16)*exp(4)-1),x, algorithm="giac")

[Out]

2*(e^x*log(400) - e^x*log(3) - e^x*log(abs(16*x*e^4 - 16*e^4 - 1)) - e^x)/(pi^2*sgn(16*x*e^4 - 16*e^4 - 1) + p
i^2 + 2*log(400)^2 - 4*log(400)*log(3) + 2*log(3)^2 - 4*log(400)*log(abs(16*x*e^4 - 16*e^4 - 1)) + 4*log(3)*lo
g(abs(16*x*e^4 - 16*e^4 - 1)) + 2*log(abs(16*x*e^4 - 16*e^4 - 1))^2 - 4*log(400) + 4*log(3) + 4*log(abs(16*x*e
^4 - 16*e^4 - 1)) + 2)

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maple [A]  time = 1.12, size = 28, normalized size = 0.97

method	result	size
default	\(-\frac {{\mathrm e}^{x}}{\ln \relax (3)-\ln \left (-\frac {400}{\left (16 x -16\right ) {\mathrm e}^{4}-1}\right )+1}\)	\(28\)
norman	\(-\frac {{\mathrm e}^{x}}{\ln \relax (3)-\ln \left (-\frac {400}{\left (16 x -16\right ) {\mathrm e}^{4}-1}\right )+1}\)	\(28\)
risch	\(-\frac {2 i {\mathrm e}^{x}}{-2 \pi \mathrm {csgn}\left (\frac {i}{-\frac {1}{16}+\left (x -1\right ) {\mathrm e}^{4}}\right )^{2}+2 \pi \mathrm {csgn}\left (\frac {i}{-\frac {1}{16}+\left (x -1\right ) {\mathrm e}^{4}}\right )^{3}+2 \pi -4 i \ln \relax (5)+2 i \ln \relax (3)+2 i \ln \left (-\frac {1}{16}+\left (x -1\right ) {\mathrm e}^{4}\right )+2 i}\)	\(74\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((16*x-16)*exp(4)-1)*exp(x)*ln(-400/((16*x-16)*exp(4)-1))+(((-16*x+16)*exp(4)+1)*ln(3)+(-16*x+32)*exp(4)+
1)*exp(x))/(((16*x-16)*exp(4)-1)*ln(-400/((16*x-16)*exp(4)-1))^2+(((-32*x+32)*exp(4)+2)*ln(3)+(-32*x+32)*exp(4
)+2)*ln(-400/((16*x-16)*exp(4)-1))+((16*x-16)*exp(4)-1)*ln(3)^2+((32*x-32)*exp(4)-2)*ln(3)+(16*x-16)*exp(4)-1)
,x,method=_RETURNVERBOSE)

[Out]

-exp(x)/(ln(3)-ln(-400/((16*x-16)*exp(4)-1))+1)

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maxima [A]  time = 0.49, size = 33, normalized size = 1.14 \begin {gather*} \frac {e^{x}}{2 \, \log \relax (5) - \log \relax (3) + 4 \, \log \relax (2) - \log \left (-16 \, x e^{4} + 16 \, e^{4} + 1\right ) - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((16*x-16)*exp(4)-1)*exp(x)*log(-400/((16*x-16)*exp(4)-1))+(((-16*x+16)*exp(4)+1)*log(3)+(-16*x+32)
*exp(4)+1)*exp(x))/(((16*x-16)*exp(4)-1)*log(-400/((16*x-16)*exp(4)-1))^2+(((-32*x+32)*exp(4)+2)*log(3)+(-32*x
+32)*exp(4)+2)*log(-400/((16*x-16)*exp(4)-1))+((16*x-16)*exp(4)-1)*log(3)^2+((32*x-32)*exp(4)-2)*log(3)+(16*x-
16)*exp(4)-1),x, algorithm="maxima")

[Out]

e^x/(2*log(5) - log(3) + 4*log(2) - log(-16*x*e^4 + 16*e^4 + 1) - 1)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {{\mathrm {e}}^x\,\left (\ln \relax (3)\,\left ({\mathrm {e}}^4\,\left (16\,x-16\right )-1\right )+{\mathrm {e}}^4\,\left (16\,x-32\right )-1\right )-{\mathrm {e}}^x\,\ln \left (-\frac {400}{{\mathrm {e}}^4\,\left (16\,x-16\right )-1}\right )\,\left ({\mathrm {e}}^4\,\left (16\,x-16\right )-1\right )}{\left ({\mathrm {e}}^4\,\left (16\,x-16\right )-1\right )\,{\ln \left (-\frac {400}{{\mathrm {e}}^4\,\left (16\,x-16\right )-1}\right )}^2+\left (2-{\mathrm {e}}^4\,\left (32\,x-32\right )-\ln \relax (3)\,\left ({\mathrm {e}}^4\,\left (32\,x-32\right )-2\right )\right )\,\ln \left (-\frac {400}{{\mathrm {e}}^4\,\left (16\,x-16\right )-1}\right )+\ln \relax (3)\,\left ({\mathrm {e}}^4\,\left (32\,x-32\right )-2\right )+{\ln \relax (3)}^2\,\left ({\mathrm {e}}^4\,\left (16\,x-16\right )-1\right )+{\mathrm {e}}^4\,\left (16\,x-16\right )-1} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(x)*(log(3)*(exp(4)*(16*x - 16) - 1) + exp(4)*(16*x - 32) - 1) - exp(x)*log(-400/(exp(4)*(16*x - 16)
- 1))*(exp(4)*(16*x - 16) - 1))/(log(3)*(exp(4)*(32*x - 32) - 2) - log(-400/(exp(4)*(16*x - 16) - 1))*(log(3)*
(exp(4)*(32*x - 32) - 2) + exp(4)*(32*x - 32) - 2) + log(3)^2*(exp(4)*(16*x - 16) - 1) + log(-400/(exp(4)*(16*
x - 16) - 1))^2*(exp(4)*(16*x - 16) - 1) + exp(4)*(16*x - 16) - 1),x)

[Out]

int(-(exp(x)*(log(3)*(exp(4)*(16*x - 16) - 1) + exp(4)*(16*x - 32) - 1) - exp(x)*log(-400/(exp(4)*(16*x - 16)
- 1))*(exp(4)*(16*x - 16) - 1))/(log(3)*(exp(4)*(32*x - 32) - 2) - log(-400/(exp(4)*(16*x - 16) - 1))*(log(3)*
(exp(4)*(32*x - 32) - 2) + exp(4)*(32*x - 32) - 2) + log(3)^2*(exp(4)*(16*x - 16) - 1) + log(-400/(exp(4)*(16*
x - 16) - 1))^2*(exp(4)*(16*x - 16) - 1) + exp(4)*(16*x - 16) - 1), x)

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sympy [A]  time = 0.62, size = 22, normalized size = 0.76 \begin {gather*} \frac {e^{x}}{\log {\left (- \frac {400}{\left (16 x - 16\right ) e^{4} - 1} \right )} - \log {\relax (3 )} - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((16*x-16)*exp(4)-1)*exp(x)*ln(-400/((16*x-16)*exp(4)-1))+(((-16*x+16)*exp(4)+1)*ln(3)+(-16*x+32)*e
xp(4)+1)*exp(x))/(((16*x-16)*exp(4)-1)*ln(-400/((16*x-16)*exp(4)-1))**2+(((-32*x+32)*exp(4)+2)*ln(3)+(-32*x+32
)*exp(4)+2)*ln(-400/((16*x-16)*exp(4)-1))+((16*x-16)*exp(4)-1)*ln(3)**2+((32*x-32)*exp(4)-2)*ln(3)+(16*x-16)*e
xp(4)-1),x)

[Out]

exp(x)/(log(-400/((16*x - 16)*exp(4) - 1)) - log(3) - 1)

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