3.43.86 \(\int \frac {e^{\frac {e^{-x} (x+x^2+3 \log (4 x^2))}{\log (4 x^2) \log (\log (4))}} (-2-2 x+(1+x-x^2) \log (4 x^2)-3 \log ^2(4 x^2))}{3 e^x \log ^2(4 x^2) \log (\log (4))+e^{x+\frac {e^{-x} (x+x^2+3 \log (4 x^2))}{\log (4 x^2) \log (\log (4))}} \log ^2(4 x^2) \log (\log (4))} \, dx\)

Optimal. Leaf size=32 \[ \log \left (3+e^{\frac {e^{-x} \left (3+\frac {x+x^2}{\log \left (4 x^2\right )}\right )}{\log (\log (4))}}\right ) \]

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Rubi [F]  time = 135.73, 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 {e^{-x} \left (x+x^2+3 \log \left (4 x^2\right )\right )}{\log \left (4 x^2\right ) \log (\log (4))}\right ) \left (-2-2 x+\left (1+x-x^2\right ) \log \left (4 x^2\right )-3 \log ^2\left (4 x^2\right )\right )}{3 e^x \log ^2\left (4 x^2\right ) \log (\log (4))+\exp \left (x+\frac {e^{-x} \left (x+x^2+3 \log \left (4 x^2\right )\right )}{\log \left (4 x^2\right ) \log (\log (4))}\right ) \log ^2\left (4 x^2\right ) \log (\log (4))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

3/(E^x*Log[Log[4]]) + (9*Defer[Int][1/(E^x*(3 + E^((x + x^2 + 3*Log[4*x^2])/(E^x*Log[4*x^2]*Log[Log[4]])))), x
])/Log[Log[4]] - (2*Defer[Int][1/(E^x*Log[4*x^2]^2), x])/Log[Log[4]] + (6*Defer[Int][1/(E^x*(3 + E^((x + x^2 +
3*Log[4*x^2])/(E^x*Log[4*x^2]*Log[Log[4]])))*Log[4*x^2]^2), x])/Log[Log[4]] - (2*Defer[Int][x/(E^x*Log[4*x^2]
^2), x])/Log[Log[4]] + (6*Defer[Int][x/(E^x*(3 + E^((x + x^2 + 3*Log[4*x^2])/(E^x*Log[4*x^2]*Log[Log[4]])))*Lo
g[4*x^2]^2), x])/Log[Log[4]] + Defer[Int][1/(E^x*Log[4*x^2]), x]/Log[Log[4]] - (3*Defer[Int][1/(E^x*(3 + E^((x
+ x^2 + 3*Log[4*x^2])/(E^x*Log[4*x^2]*Log[Log[4]])))*Log[4*x^2]), x])/Log[Log[4]] + Defer[Int][x/(E^x*Log[4*x
^2]), x]/Log[Log[4]] - (3*Defer[Int][x/(E^x*(3 + E^((x + x^2 + 3*Log[4*x^2])/(E^x*Log[4*x^2]*Log[Log[4]])))*Lo
g[4*x^2]), x])/Log[Log[4]] - Defer[Int][x^2/(E^x*Log[4*x^2]), x]/Log[Log[4]] + (3*Defer[Int][x^2/(E^x*(3 + E^(
(x + x^2 + 3*Log[4*x^2])/(E^x*Log[4*x^2]*Log[Log[4]])))*Log[4*x^2]), x])/Log[Log[4]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-x} \left (-2 (1+x)+\left (1+x-x^2\right ) \log \left (4 x^2\right )-3 \log ^2\left (4 x^2\right )\right )}{\left (1+3 \exp \left (-\frac {e^{-x} \left (x+x^2+3 \log \left (4 x^2\right )\right )}{\log \left (4 x^2\right ) \log (\log (4))}\right )\right ) \log ^2\left (4 x^2\right ) \log (\log (4))} \, dx\\ &=\frac {\int \frac {e^{-x} \left (-2 (1+x)+\left (1+x-x^2\right ) \log \left (4 x^2\right )-3 \log ^2\left (4 x^2\right )\right )}{\left (1+3 \exp \left (-\frac {e^{-x} \left (x+x^2+3 \log \left (4 x^2\right )\right )}{\log \left (4 x^2\right ) \log (\log (4))}\right )\right ) \log ^2\left (4 x^2\right )} \, dx}{\log (\log (4))}\\ &=\frac {\int \left (\frac {e^{-x} \left (-2-2 x+\log \left (4 x^2\right )+x \log \left (4 x^2\right )-x^2 \log \left (4 x^2\right )-3 \log ^2\left (4 x^2\right )\right )}{\log ^2\left (4 x^2\right )}+\frac {3 e^{-x} \left (2+2 x-\log \left (4 x^2\right )-x \log \left (4 x^2\right )+x^2 \log \left (4 x^2\right )+3 \log ^2\left (4 x^2\right )\right )}{\left (3+\exp \left (\frac {3 e^{-x}}{\log (\log (4))}+\frac {e^{-x} x}{\log \left (4 x^2\right ) \log (\log (4))}+\frac {e^{-x} x^2}{\log \left (4 x^2\right ) \log (\log (4))}\right )\right ) \log ^2\left (4 x^2\right )}\right ) \, dx}{\log (\log (4))}\\ &=\frac {\int \frac {e^{-x} \left (-2-2 x+\log \left (4 x^2\right )+x \log \left (4 x^2\right )-x^2 \log \left (4 x^2\right )-3 \log ^2\left (4 x^2\right )\right )}{\log ^2\left (4 x^2\right )} \, dx}{\log (\log (4))}+\frac {3 \int \frac {e^{-x} \left (2+2 x-\log \left (4 x^2\right )-x \log \left (4 x^2\right )+x^2 \log \left (4 x^2\right )+3 \log ^2\left (4 x^2\right )\right )}{\left (3+\exp \left (\frac {3 e^{-x}}{\log (\log (4))}+\frac {e^{-x} x}{\log \left (4 x^2\right ) \log (\log (4))}+\frac {e^{-x} x^2}{\log \left (4 x^2\right ) \log (\log (4))}\right )\right ) \log ^2\left (4 x^2\right )} \, dx}{\log (\log (4))}\\ &=\frac {\int \left (-3 e^{-x}-\frac {2 e^{-x} (1+x)}{\log ^2\left (4 x^2\right )}+\frac {e^{-x} \left (1+x-x^2\right )}{\log \left (4 x^2\right )}\right ) \, dx}{\log (\log (4))}+\frac {3 \int \frac {e^{-x} \left (2 (1+x)+\left (-1-x+x^2\right ) \log \left (4 x^2\right )+3 \log ^2\left (4 x^2\right )\right )}{\left (3+\exp \left (\frac {e^{-x} \left (x+x^2+3 \log \left (4 x^2\right )\right )}{\log \left (4 x^2\right ) \log (\log (4))}\right )\right ) \log ^2\left (4 x^2\right )} \, dx}{\log (\log (4))}\\ &=\frac {\int \frac {e^{-x} \left (1+x-x^2\right )}{\log \left (4 x^2\right )} \, dx}{\log (\log (4))}-\frac {2 \int \frac {e^{-x} (1+x)}{\log ^2\left (4 x^2\right )} \, dx}{\log (\log (4))}-\frac {3 \int e^{-x} \, dx}{\log (\log (4))}+\frac {3 \int \left (\frac {3 e^{-x}}{3+\exp \left (\frac {3 e^{-x}}{\log (\log (4))}+\frac {e^{-x} x}{\log \left (4 x^2\right ) \log (\log (4))}+\frac {e^{-x} x^2}{\log \left (4 x^2\right ) \log (\log (4))}\right )}+\frac {2 e^{-x}}{\left (3+\exp \left (\frac {3 e^{-x}}{\log (\log (4))}+\frac {e^{-x} x}{\log \left (4 x^2\right ) \log (\log (4))}+\frac {e^{-x} x^2}{\log \left (4 x^2\right ) \log (\log (4))}\right )\right ) \log ^2\left (4 x^2\right )}+\frac {2 e^{-x} x}{\left (3+\exp \left (\frac {3 e^{-x}}{\log (\log (4))}+\frac {e^{-x} x}{\log \left (4 x^2\right ) \log (\log (4))}+\frac {e^{-x} x^2}{\log \left (4 x^2\right ) \log (\log (4))}\right )\right ) \log ^2\left (4 x^2\right )}-\frac {e^{-x}}{\left (3+\exp \left (\frac {3 e^{-x}}{\log (\log (4))}+\frac {e^{-x} x}{\log \left (4 x^2\right ) \log (\log (4))}+\frac {e^{-x} x^2}{\log \left (4 x^2\right ) \log (\log (4))}\right )\right ) \log \left (4 x^2\right )}-\frac {e^{-x} x}{\left (3+\exp \left (\frac {3 e^{-x}}{\log (\log (4))}+\frac {e^{-x} x}{\log \left (4 x^2\right ) \log (\log (4))}+\frac {e^{-x} x^2}{\log \left (4 x^2\right ) \log (\log (4))}\right )\right ) \log \left (4 x^2\right )}+\frac {e^{-x} x^2}{\left (3+\exp \left (\frac {3 e^{-x}}{\log (\log (4))}+\frac {e^{-x} x}{\log \left (4 x^2\right ) \log (\log (4))}+\frac {e^{-x} x^2}{\log \left (4 x^2\right ) \log (\log (4))}\right )\right ) \log \left (4 x^2\right )}\right ) \, dx}{\log (\log (4))}\\ &=\frac {3 e^{-x}}{\log (\log (4))}+\frac {\int \left (\frac {e^{-x}}{\log \left (4 x^2\right )}+\frac {e^{-x} x}{\log \left (4 x^2\right )}-\frac {e^{-x} x^2}{\log \left (4 x^2\right )}\right ) \, dx}{\log (\log (4))}-\frac {2 \int \left (\frac {e^{-x}}{\log ^2\left (4 x^2\right )}+\frac {e^{-x} x}{\log ^2\left (4 x^2\right )}\right ) \, dx}{\log (\log (4))}-\frac {3 \int \frac {e^{-x}}{\left (3+\exp \left (\frac {3 e^{-x}}{\log (\log (4))}+\frac {e^{-x} x}{\log \left (4 x^2\right ) \log (\log (4))}+\frac {e^{-x} x^2}{\log \left (4 x^2\right ) \log (\log (4))}\right )\right ) \log \left (4 x^2\right )} \, dx}{\log (\log (4))}-\frac {3 \int \frac {e^{-x} x}{\left (3+\exp \left (\frac {3 e^{-x}}{\log (\log (4))}+\frac {e^{-x} x}{\log \left (4 x^2\right ) \log (\log (4))}+\frac {e^{-x} x^2}{\log \left (4 x^2\right ) \log (\log (4))}\right )\right ) \log \left (4 x^2\right )} \, dx}{\log (\log (4))}+\frac {3 \int \frac {e^{-x} x^2}{\left (3+\exp \left (\frac {3 e^{-x}}{\log (\log (4))}+\frac {e^{-x} x}{\log \left (4 x^2\right ) \log (\log (4))}+\frac {e^{-x} x^2}{\log \left (4 x^2\right ) \log (\log (4))}\right )\right ) \log \left (4 x^2\right )} \, dx}{\log (\log (4))}+\frac {6 \int \frac {e^{-x}}{\left (3+\exp \left (\frac {3 e^{-x}}{\log (\log (4))}+\frac {e^{-x} x}{\log \left (4 x^2\right ) \log (\log (4))}+\frac {e^{-x} x^2}{\log \left (4 x^2\right ) \log (\log (4))}\right )\right ) \log ^2\left (4 x^2\right )} \, dx}{\log (\log (4))}+\frac {6 \int \frac {e^{-x} x}{\left (3+\exp \left (\frac {3 e^{-x}}{\log (\log (4))}+\frac {e^{-x} x}{\log \left (4 x^2\right ) \log (\log (4))}+\frac {e^{-x} x^2}{\log \left (4 x^2\right ) \log (\log (4))}\right )\right ) \log ^2\left (4 x^2\right )} \, dx}{\log (\log (4))}+\frac {9 \int \frac {e^{-x}}{3+\exp \left (\frac {3 e^{-x}}{\log (\log (4))}+\frac {e^{-x} x}{\log \left (4 x^2\right ) \log (\log (4))}+\frac {e^{-x} x^2}{\log \left (4 x^2\right ) \log (\log (4))}\right )} \, dx}{\log (\log (4))}\\ &=\frac {3 e^{-x}}{\log (\log (4))}+\frac {\int \frac {e^{-x}}{\log \left (4 x^2\right )} \, dx}{\log (\log (4))}+\frac {\int \frac {e^{-x} x}{\log \left (4 x^2\right )} \, dx}{\log (\log (4))}-\frac {\int \frac {e^{-x} x^2}{\log \left (4 x^2\right )} \, dx}{\log (\log (4))}-\frac {2 \int \frac {e^{-x}}{\log ^2\left (4 x^2\right )} \, dx}{\log (\log (4))}-\frac {2 \int \frac {e^{-x} x}{\log ^2\left (4 x^2\right )} \, dx}{\log (\log (4))}-\frac {3 \int \frac {e^{-x}}{\left (3+\exp \left (\frac {e^{-x} \left (x+x^2+3 \log \left (4 x^2\right )\right )}{\log \left (4 x^2\right ) \log (\log (4))}\right )\right ) \log \left (4 x^2\right )} \, dx}{\log (\log (4))}-\frac {3 \int \frac {e^{-x} x}{\left (3+\exp \left (\frac {e^{-x} \left (x+x^2+3 \log \left (4 x^2\right )\right )}{\log \left (4 x^2\right ) \log (\log (4))}\right )\right ) \log \left (4 x^2\right )} \, dx}{\log (\log (4))}+\frac {3 \int \frac {e^{-x} x^2}{\left (3+\exp \left (\frac {e^{-x} \left (x+x^2+3 \log \left (4 x^2\right )\right )}{\log \left (4 x^2\right ) \log (\log (4))}\right )\right ) \log \left (4 x^2\right )} \, dx}{\log (\log (4))}+\frac {6 \int \frac {e^{-x}}{\left (3+\exp \left (\frac {e^{-x} \left (x+x^2+3 \log \left (4 x^2\right )\right )}{\log \left (4 x^2\right ) \log (\log (4))}\right )\right ) \log ^2\left (4 x^2\right )} \, dx}{\log (\log (4))}+\frac {6 \int \frac {e^{-x} x}{\left (3+\exp \left (\frac {e^{-x} \left (x+x^2+3 \log \left (4 x^2\right )\right )}{\log \left (4 x^2\right ) \log (\log (4))}\right )\right ) \log ^2\left (4 x^2\right )} \, dx}{\log (\log (4))}+\frac {9 \int \frac {e^{-x}}{3+\exp \left (\frac {e^{-x} \left (x+x^2+3 \log \left (4 x^2\right )\right )}{\log \left (4 x^2\right ) \log (\log (4))}\right )} \, dx}{\log (\log (4))}\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 1.20, size = 82, normalized size = 2.56 \begin {gather*} \frac {3 e^{-x}}{\log (\log (4))}+\frac {\frac {e^{-x} x (1+x)}{\log \left (4 x^2\right )}+\log \left (1+3 e^{-\frac {e^{-x} \left (x+x^2+3 \log \left (4 x^2\right )\right )}{\log \left (4 x^2\right ) \log (\log (4))}}\right ) \log (\log (4))}{\log (\log (4))} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

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

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fricas [A]  time = 0.60, size = 59, normalized size = 1.84 \begin {gather*} -x + \log \left (3 \, e^{x} + e^{\left (\frac {{\left (x e^{x} \log \left (4 \, x^{2}\right ) \log \left (2 \, \log \relax (2)\right ) + x^{2} + x + 3 \, \log \left (4 \, x^{2}\right )\right )} e^{\left (-x\right )}}{\log \left (4 \, x^{2}\right ) \log \left (2 \, \log \relax (2)\right )}\right )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x + log(3*e^x + e^((x*e^x*log(4*x^2)*log(2*log(2)) + x^2 + x + 3*log(4*x^2))*e^(-x)/(log(4*x^2)*log(2*log(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((-3*log(4*x^2)^2+(-x^2+x+1)*log(4*x^2)-2*x-2)*exp((3*log(4*x^2)+x^2+x)/exp(x)/log(4*x^2)/log(2*log(2
)))/(exp(x)*log(4*x^2)^2*log(2*log(2))*exp((3*log(4*x^2)+x^2+x)/exp(x)/log(4*x^2)/log(2*log(2)))+3*exp(x)*log(
4*x^2)^2*log(2*log(2))),x, algorithm="giac")

[Out]

undef

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maple [C]  time = 6.01, size = 329, normalized size = 10.28

method	result	size
risch	\(\frac {3 \,{\mathrm e}^{-x}}{\ln \relax (2)+\ln \left (\ln \relax (2)\right )}+\frac {2 i \left (x +1\right ) x \,{\mathrm e}^{-x}}{\left (\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}+4 i \ln \relax (2)+4 i \ln \relax (x )\right ) \left (\ln \relax (2)+\ln \left (\ln \relax (2)\right )\right )}-\frac {\left (6 \ln \relax (2)+6 \ln \relax (x )-\frac {3 i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (-\mathrm {csgn}\left (i x^{2}\right )+\mathrm {csgn}\left (i x \right )\right )^{2}}{2}+x^{2}+x \right ) {\mathrm e}^{-x}}{\left (2 \ln \relax (2)+2 \ln \relax (x )-\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (-\mathrm {csgn}\left (i x^{2}\right )+\mathrm {csgn}\left (i x \right )\right )^{2}}{2}\right ) \left (\ln \relax (2)+\ln \left (\ln \relax (2)\right )\right )}+\ln \left ({\mathrm e}^{\frac {\left (-3 i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+6 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-3 i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+2 x^{2}+12 \ln \relax (2)+12 \ln \relax (x )+2 x \right ) {\mathrm e}^{-x}}{\left (-i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+2 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+4 \ln \relax (2)+4 \ln \relax (x )\right ) \left (\ln \relax (2)+\ln \left (\ln \relax (2)\right )\right )}}+3\right )\)	\(329\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3*exp(-x)/(ln(2)+ln(ln(2)))+2*I*(x+1)*x/(Pi*csgn(I*x)^2*csgn(I*x^2)-2*Pi*csgn(I*x)*csgn(I*x^2)^2+Pi*csgn(I*x^2
)^3+4*I*ln(2)+4*I*ln(x))*exp(-x)/(ln(2)+ln(ln(2)))-(6*ln(2)+6*ln(x)-3/2*I*Pi*csgn(I*x^2)*(-csgn(I*x^2)+csgn(I*
x))^2+x^2+x)*exp(-x)/(2*ln(2)+2*ln(x)-1/2*I*Pi*csgn(I*x^2)*(-csgn(I*x^2)+csgn(I*x))^2)/(ln(2)+ln(ln(2)))+ln(ex
p((-3*I*Pi*csgn(I*x^2)^3+6*I*Pi*csgn(I*x^2)^2*csgn(I*x)-3*I*Pi*csgn(I*x^2)*csgn(I*x)^2+2*x^2+12*ln(2)+12*ln(x)
+2*x)*exp(-x)/(-I*Pi*csgn(I*x^2)^3+2*I*Pi*csgn(I*x)*csgn(I*x^2)^2-I*Pi*csgn(I*x)^2*csgn(I*x^2)+4*ln(2)+4*ln(x)
)/(ln(2)+ln(ln(2))))+3)

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maxima [B]  time = 0.70, size = 170, normalized size = 5.31 \begin {gather*} \frac {{\left (x + 6 \, \log \relax (2) + 6 \, \log \relax (x)\right )} e^{\left (-x\right )}}{2 \, {\left (\log \relax (2)^{2} + {\left (\log \relax (2) + \log \left (\log \relax (2)\right )\right )} \log \relax (x) + \log \relax (2) \log \left (\log \relax (2)\right )\right )}} + \log \left ({\left (e^{\left (\frac {x^{2}}{2 \, {\left ({\left (\log \relax (2) + \log \left (\log \relax (2)\right )\right )} e^{x} \log \relax (x) + {\left (\log \relax (2)^{2} + \log \relax (2) \log \left (\log \relax (2)\right )\right )} e^{x}\right )}} + \frac {x}{2 \, {\left ({\left (\log \relax (2) + \log \left (\log \relax (2)\right )\right )} e^{x} \log \relax (x) + {\left (\log \relax (2)^{2} + \log \relax (2) \log \left (\log \relax (2)\right )\right )} e^{x}\right )}} + \frac {3 \, e^{\left (-x\right )}}{\log \relax (2) + \log \left (\log \relax (2)\right )}\right )} + 3\right )} e^{\left (-\frac {x}{2 \, {\left ({\left (\log \relax (2) + \log \left (\log \relax (2)\right )\right )} e^{x} \log \relax (x) + {\left (\log \relax (2)^{2} + \log \relax (2) \log \left (\log \relax (2)\right )\right )} e^{x}\right )}} - \frac {3 \, e^{\left (-x\right )}}{\log \relax (2) + \log \left (\log \relax (2)\right )}\right )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*(x + 6*log(2) + 6*log(x))*e^(-x)/(log(2)^2 + (log(2) + log(log(2)))*log(x) + log(2)*log(log(2))) + log((e^
(1/2*x^2/((log(2) + log(log(2)))*e^x*log(x) + (log(2)^2 + log(2)*log(log(2)))*e^x) + 1/2*x/((log(2) + log(log(
2)))*e^x*log(x) + (log(2)^2 + log(2)*log(log(2)))*e^x) + 3*e^(-x)/(log(2) + log(log(2)))) + 3)*e^(-1/2*x/((log
(2) + log(log(2)))*e^x*log(x) + (log(2)^2 + log(2)*log(log(2)))*e^x) - 3*e^(-x)/(log(2) + log(log(2)))))

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mupad [B]  time = 3.79, size = 107, normalized size = 3.34 \begin {gather*} \ln \left ({\mathrm {e}}^{\frac {{\mathrm {e}}^{-x}\,\ln \left (64\,x^6\right )}{\ln \relax (4)\,\ln \left (\ln \relax (2)\right )+2\,{\ln \relax (2)}^2+\ln \left (2\,\ln \relax (2)\right )\,\ln \left (x^2\right )}}\,{\mathrm {e}}^{\frac {x^2\,{\mathrm {e}}^{-x}}{\ln \relax (4)\,\ln \left (\ln \relax (2)\right )+2\,{\ln \relax (2)}^2+\ln \left (2\,\ln \relax (2)\right )\,\ln \left (x^2\right )}}\,{\mathrm {e}}^{\frac {x\,{\mathrm {e}}^{-x}}{\ln \relax (4)\,\ln \left (\ln \relax (2)\right )+2\,{\ln \relax (2)}^2+\ln \left (2\,\ln \relax (2)\right )\,\ln \left (x^2\right )}}+3\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

log(exp((exp(-x)*log(64*x^6))/(log(4)*log(log(2)) + 2*log(2)^2 + log(2*log(2))*log(x^2)))*exp((x^2*exp(-x))/(l
og(4)*log(log(2)) + 2*log(2)^2 + log(2*log(2))*log(x^2)))*exp((x*exp(-x))/(log(4)*log(log(2)) + 2*log(2)^2 + l
og(2*log(2))*log(x^2))) + 3)

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sympy [A]  time = 1.22, size = 34, normalized size = 1.06 \begin {gather*} \log {\left (e^{\frac {\left (x^{2} + x + 3 \log {\left (4 x^{2} \right )}\right ) e^{- x}}{\log {\left (4 x^{2} \right )} \log {\left (2 \log {\relax (2 )} \right )}}} + 3 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

log(exp((x**2 + x + 3*log(4*x**2))*exp(-x)/(log(4*x**2)*log(2*log(2)))) + 3)

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