3.23.29 \(\int \frac {36+72 x+48 x^3-4 x^4+8 x^5+(-9 x-6 x^3-x^5+e^{4 x} (6 x^3-x^3 \log (4))) \log ^2(\frac {e^{-4 x} (9+6 x^2+x^4+e^{4 x} (-6 x^2+x^2 \log (4)))}{x^2})}{(9 x+6 x^3+x^5+e^{4 x} (-6 x^3+x^3 \log (4))) \log ^2(\frac {e^{-4 x} (9+6 x^2+x^4+e^{4 x} (-6 x^2+x^2 \log (4)))}{x^2})} \, dx\)

Optimal. Leaf size=28 \[ -x+\frac {2}{\log \left (-6+e^{-4 x} \left (\frac {3}{x}+x\right )^2+\log (4)\right )} \]

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Rubi [F]  time = 5.91, 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 {36+72 x+48 x^3-4 x^4+8 x^5+\left (-9 x-6 x^3-x^5+e^{4 x} \left (6 x^3-x^3 \log (4)\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+6 x^2+x^4+e^{4 x} \left (-6 x^2+x^2 \log (4)\right )\right )}{x^2}\right )}{\left (9 x+6 x^3+x^5+e^{4 x} \left (-6 x^3+x^3 \log (4)\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+6 x^2+x^4+e^{4 x} \left (-6 x^2+x^2 \log (4)\right )\right )}{x^2}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(36 + 72*x + 48*x^3 - 4*x^4 + 8*x^5 + (-9*x - 6*x^3 - x^5 + E^(4*x)*(6*x^3 - x^3*Log[4]))*Log[(9 + 6*x^2 +
x^4 + E^(4*x)*(-6*x^2 + x^2*Log[4]))/(E^(4*x)*x^2)]^2)/((9*x + 6*x^3 + x^5 + E^(4*x)*(-6*x^3 + x^3*Log[4]))*L
og[(9 + 6*x^2 + x^4 + E^(4*x)*(-6*x^2 + x^2*Log[4]))/(E^(4*x)*x^2)]^2),x]

[Out]

-x + 72*Defer[Int][1/((9 + 6*x^2 + x^4 - 6*E^(4*x)*x^2*(1 - Log[2]/3))*Log[(9 + x^4 + x^2*(6 + E^(4*x)*(-6 + L
og[4])))/(E^(4*x)*x^2)]^2), x] + 36*Defer[Int][1/(x*(9 + 6*x^2 + x^4 - 6*E^(4*x)*x^2*(1 - Log[2]/3))*Log[(9 +
x^4 + x^2*(6 + E^(4*x)*(-6 + Log[4])))/(E^(4*x)*x^2)]^2), x] + 48*Defer[Int][x^2/((9 + 6*x^2 + x^4 - 6*E^(4*x)
*x^2*(1 - Log[2]/3))*Log[(9 + x^4 + x^2*(6 + E^(4*x)*(-6 + Log[4])))/(E^(4*x)*x^2)]^2), x] + 8*Defer[Int][x^4/
((9 + 6*x^2 + x^4 - 6*E^(4*x)*x^2*(1 - Log[2]/3))*Log[(9 + x^4 + x^2*(6 + E^(4*x)*(-6 + Log[4])))/(E^(4*x)*x^2
)]^2), x] + 4*Defer[Int][x^3/((-9 - 6*x^2 - x^4 + 6*E^(4*x)*x^2*(1 - Log[2]/3))*Log[(9 + x^4 + x^2*(6 + E^(4*x
)*(-6 + Log[4])))/(E^(4*x)*x^2)]^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1+\frac {4 \left (3+x^2\right ) \left (3+6 x-x^2+2 x^3\right )}{x \left (9+6 x^2+x^4-6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )}\right ) \, dx\\ &=-x+4 \int \frac {\left (3+x^2\right ) \left (3+6 x-x^2+2 x^3\right )}{x \left (9+6 x^2+x^4-6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )} \, dx\\ &=-x+4 \int \left (\frac {18}{\left (9+6 x^2+x^4-6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )}+\frac {9}{x \left (9+6 x^2+x^4-6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )}+\frac {12 x^2}{\left (9+6 x^2+x^4-6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )}+\frac {2 x^4}{\left (9+6 x^2+x^4-6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )}+\frac {x^3}{\left (-9-6 x^2-x^4+6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )}\right ) \, dx\\ &=-x+4 \int \frac {x^3}{\left (-9-6 x^2-x^4+6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )} \, dx+8 \int \frac {x^4}{\left (9+6 x^2+x^4-6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )} \, dx+36 \int \frac {1}{x \left (9+6 x^2+x^4-6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )} \, dx+48 \int \frac {x^2}{\left (9+6 x^2+x^4-6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )} \, dx+72 \int \frac {1}{\left (9+6 x^2+x^4-6 e^{4 x} x^2 \left (1-\frac {\log (2)}{3}\right )\right ) \log ^2\left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.10, size = 39, normalized size = 1.39 \begin {gather*} -x+\frac {2}{\log \left (\frac {e^{-4 x} \left (9+x^4+x^2 \left (6+e^{4 x} (-6+\log (4))\right )\right )}{x^2}\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(36 + 72*x + 48*x^3 - 4*x^4 + 8*x^5 + (-9*x - 6*x^3 - x^5 + E^(4*x)*(6*x^3 - x^3*Log[4]))*Log[(9 + 6
*x^2 + x^4 + E^(4*x)*(-6*x^2 + x^2*Log[4]))/(E^(4*x)*x^2)]^2)/((9*x + 6*x^3 + x^5 + E^(4*x)*(-6*x^3 + x^3*Log[
4]))*Log[(9 + 6*x^2 + x^4 + E^(4*x)*(-6*x^2 + x^2*Log[4]))/(E^(4*x)*x^2)]^2),x]

[Out]

-x + 2/Log[(9 + x^4 + x^2*(6 + E^(4*x)*(-6 + Log[4])))/(E^(4*x)*x^2)]

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fricas [B]  time = 0.67, size = 82, normalized size = 2.93 \begin {gather*} -\frac {x \log \left (\frac {{\left (x^{4} + 6 \, x^{2} + 2 \, {\left (x^{2} \log \relax (2) - 3 \, x^{2}\right )} e^{\left (4 \, x\right )} + 9\right )} e^{\left (-4 \, x\right )}}{x^{2}}\right ) - 2}{\log \left (\frac {{\left (x^{4} + 6 \, x^{2} + 2 \, {\left (x^{2} \log \relax (2) - 3 \, x^{2}\right )} e^{\left (4 \, x\right )} + 9\right )} e^{\left (-4 \, x\right )}}{x^{2}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^3*log(2)+6*x^3)*exp(x)^4-x^5-6*x^3-9*x)*log(((2*x^2*log(2)-6*x^2)*exp(x)^4+x^4+6*x^2+9)/x^2/
exp(x)^4)^2+8*x^5-4*x^4+48*x^3+72*x+36)/((2*x^3*log(2)-6*x^3)*exp(x)^4+x^5+6*x^3+9*x)/log(((2*x^2*log(2)-6*x^2
)*exp(x)^4+x^4+6*x^2+9)/x^2/exp(x)^4)^2,x, algorithm="fricas")

[Out]

-(x*log((x^4 + 6*x^2 + 2*(x^2*log(2) - 3*x^2)*e^(4*x) + 9)*e^(-4*x)/x^2) - 2)/log((x^4 + 6*x^2 + 2*(x^2*log(2)
- 3*x^2)*e^(4*x) + 9)*e^(-4*x)/x^2)

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giac [B]  time = 5.07, size = 94, normalized size = 3.36 \begin {gather*} -\frac {x \log \left (x^{2}\right ) - x \log \left ({\left (x^{4} + 2 \, x^{2} e^{\left (4 \, x\right )} \log \relax (2) - 6 \, x^{2} e^{\left (4 \, x\right )} + 6 \, x^{2} + 9\right )} e^{\left (-4 \, x\right )}\right ) + 2}{\log \left (x^{2}\right ) - \log \left ({\left (x^{4} + 2 \, x^{2} e^{\left (4 \, x\right )} \log \relax (2) - 6 \, x^{2} e^{\left (4 \, x\right )} + 6 \, x^{2} + 9\right )} e^{\left (-4 \, x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^3*log(2)+6*x^3)*exp(x)^4-x^5-6*x^3-9*x)*log(((2*x^2*log(2)-6*x^2)*exp(x)^4+x^4+6*x^2+9)/x^2/
exp(x)^4)^2+8*x^5-4*x^4+48*x^3+72*x+36)/((2*x^3*log(2)-6*x^3)*exp(x)^4+x^5+6*x^3+9*x)/log(((2*x^2*log(2)-6*x^2
)*exp(x)^4+x^4+6*x^2+9)/x^2/exp(x)^4)^2,x, algorithm="giac")

[Out]

-(x*log(x^2) - x*log((x^4 + 2*x^2*e^(4*x)*log(2) - 6*x^2*e^(4*x) + 6*x^2 + 9)*e^(-4*x)) + 2)/(log(x^2) - log((
x^4 + 2*x^2*e^(4*x)*log(2) - 6*x^2*e^(4*x) + 6*x^2 + 9)*e^(-4*x)))

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maple [B]  time = 0.81, size = 83, normalized size = 2.96

method	result	size
norman	\(\frac {2-x \ln \left (\frac {\left (\left (2 x^{2} \ln \relax (2)-6 x^{2}\right ) {\mathrm e}^{4 x}+x^{4}+6 x^{2}+9\right ) {\mathrm e}^{-4 x}}{x^{2}}\right )}{\ln \left (\frac {\left (\left (2 x^{2} \ln \relax (2)-6 x^{2}\right ) {\mathrm e}^{4 x}+x^{4}+6 x^{2}+9\right ) {\mathrm e}^{-4 x}}{x^{2}}\right )}\)	\(83\)
risch	\(-x +\frac {4 i}{\pi \,\mathrm {csgn}\left (i \left ({\mathrm e}^{4 x} \ln \relax (2) x^{2}+\frac {9}{2}+\frac {x^{4}}{2}+\left (-3 \,{\mathrm e}^{4 x}+3\right ) x^{2}\right )\right ) \mathrm {csgn}\left (i {\mathrm e}^{-4 x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{-4 x} \left ({\mathrm e}^{4 x} \ln \relax (2) x^{2}+\frac {9}{2}+\frac {x^{4}}{2}+\left (-3 \,{\mathrm e}^{4 x}+3\right ) x^{2}\right )\right )+\pi \,\mathrm {csgn}\left (i {\mathrm e}^{-4 x} \left ({\mathrm e}^{4 x} \ln \relax (2) x^{2}+\frac {9}{2}+\frac {x^{4}}{2}+\left (-3 \,{\mathrm e}^{4 x}+3\right ) x^{2}\right )\right ) \mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{4 x} \ln \relax (2) x^{2}+\frac {9}{2}+\frac {x^{4}}{2}+\left (-3 \,{\mathrm e}^{4 x}+3\right ) x^{2}\right ) {\mathrm e}^{-4 x}}{x^{2}}\right ) \mathrm {csgn}\left (\frac {i}{x^{2}}\right )-\pi \,\mathrm {csgn}\left (i {\mathrm e}^{x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{3 x}\right )-\pi \,\mathrm {csgn}\left (i {\mathrm e}^{x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{3 x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{4 x}\right )+2 i \ln \relax (2)-4 i \ln \relax (x )-\pi \mathrm {csgn}\left (i x^{2}\right )^{3}-\pi \mathrm {csgn}\left (i {\mathrm e}^{3 x}\right )^{3}-\pi \mathrm {csgn}\left (i {\mathrm e}^{4 x}\right )^{3}-8 i \ln \left ({\mathrm e}^{x}\right )+\pi \mathrm {csgn}\left (i {\mathrm e}^{-4 x} \left ({\mathrm e}^{4 x} \ln \relax (2) x^{2}+\frac {9}{2}+\frac {x^{4}}{2}+\left (-3 \,{\mathrm e}^{4 x}+3\right ) x^{2}\right )\right )^{3}-\pi \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right )^{3}+\pi \mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{4 x} \ln \relax (2) x^{2}+\frac {9}{2}+\frac {x^{4}}{2}+\left (-3 \,{\mathrm e}^{4 x}+3\right ) x^{2}\right ) {\mathrm e}^{-4 x}}{x^{2}}\right )^{3}+2 i \ln \left ({\mathrm e}^{4 x} \ln \relax (2) x^{2}+\frac {9}{2}+\frac {x^{4}}{2}+\left (-3 \,{\mathrm e}^{4 x}+3\right ) x^{2}\right )-\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 \left ({\mathrm e}^{4 x} \ln \relax (2) x^{2}+\frac {9}{2}+\frac {x^{4}}{2}+\left (-3 \,{\mathrm e}^{4 x}+3\right ) x^{2}\right )\right ) \mathrm {csgn}\left (i {\mathrm e}^{-4 x} \left ({\mathrm e}^{4 x} \ln \relax (2) x^{2}+\frac {9}{2}+\frac {x^{4}}{2}+\left (-3 \,{\mathrm e}^{4 x}+3\right ) x^{2}\right )\right )^{2}-\pi \,\mathrm {csgn}\left (i {\mathrm e}^{-4 x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{-4 x} \left ({\mathrm e}^{4 x} \ln \relax (2) x^{2}+\frac {9}{2}+\frac {x^{4}}{2}+\left (-3 \,{\mathrm e}^{4 x}+3\right ) x^{2}\right )\right )^{2}+2 \pi \,\mathrm {csgn}\left (i {\mathrm e}^{x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right )^{2}+\pi \,\mathrm {csgn}\left (i {\mathrm e}^{3 x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{4 x}\right )^{2}-\pi \mathrm {csgn}\left (i {\mathrm e}^{x}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right )+\pi \,\mathrm {csgn}\left (i {\mathrm e}^{x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{3 x}\right )^{2}+\pi \,\mathrm {csgn}\left (i {\mathrm e}^{x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{4 x}\right )^{2}+\pi \,\mathrm {csgn}\left (i {\mathrm e}^{2 x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{3 x}\right )^{2}-\pi \,\mathrm {csgn}\left (i {\mathrm e}^{-4 x} \left ({\mathrm e}^{4 x} \ln \relax (2) x^{2}+\frac {9}{2}+\frac {x^{4}}{2}+\left (-3 \,{\mathrm e}^{4 x}+3\right ) x^{2}\right )\right ) \mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{4 x} \ln \relax (2) x^{2}+\frac {9}{2}+\frac {x^{4}}{2}+\left (-3 \,{\mathrm e}^{4 x}+3\right ) x^{2}\right ) {\mathrm e}^{-4 x}}{x^{2}}\right )^{2}-\pi \mathrm {csgn}\left (\frac {i \left ({\mathrm e}^{4 x} \ln \relax (2) x^{2}+\frac {9}{2}+\frac {x^{4}}{2}+\left (-3 \,{\mathrm e}^{4 x}+3\right ) x^{2}\right ) {\mathrm e}^{-4 x}}{x^{2}}\right )^{2} \mathrm {csgn}\left (\frac {i}{x^{2}}\right )}\)	\(819\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-2*x^3*ln(2)+6*x^3)*exp(x)^4-x^5-6*x^3-9*x)*ln(((2*x^2*ln(2)-6*x^2)*exp(x)^4+x^4+6*x^2+9)/x^2/exp(x)^4)
^2+8*x^5-4*x^4+48*x^3+72*x+36)/((2*x^3*ln(2)-6*x^3)*exp(x)^4+x^5+6*x^3+9*x)/ln(((2*x^2*ln(2)-6*x^2)*exp(x)^4+x
^4+6*x^2+9)/x^2/exp(x)^4)^2,x,method=_RETURNVERBOSE)

[Out]

(2-x*ln(((2*x^2*ln(2)-6*x^2)*exp(x)^4+x^4+6*x^2+9)/x^2/exp(x)^4))/ln(((2*x^2*ln(2)-6*x^2)*exp(x)^4+x^4+6*x^2+9
)/x^2/exp(x)^4)

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maxima [B]  time = 0.73, size = 77, normalized size = 2.75 \begin {gather*} -\frac {4 \, x^{2} - x \log \left (x^{4} + 2 \, x^{2} {\left (\log \relax (2) - 3\right )} e^{\left (4 \, x\right )} + 6 \, x^{2} + 9\right ) + 2 \, x \log \relax (x) + 2}{4 \, x - \log \left (x^{4} + 2 \, x^{2} {\left (\log \relax (2) - 3\right )} e^{\left (4 \, x\right )} + 6 \, x^{2} + 9\right ) + 2 \, \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^3*log(2)+6*x^3)*exp(x)^4-x^5-6*x^3-9*x)*log(((2*x^2*log(2)-6*x^2)*exp(x)^4+x^4+6*x^2+9)/x^2/
exp(x)^4)^2+8*x^5-4*x^4+48*x^3+72*x+36)/((2*x^3*log(2)-6*x^3)*exp(x)^4+x^5+6*x^3+9*x)/log(((2*x^2*log(2)-6*x^2
)*exp(x)^4+x^4+6*x^2+9)/x^2/exp(x)^4)^2,x, algorithm="maxima")

[Out]

-(4*x^2 - x*log(x^4 + 2*x^2*(log(2) - 3)*e^(4*x) + 6*x^2 + 9) + 2*x*log(x) + 2)/(4*x - log(x^4 + 2*x^2*(log(2)
- 3)*e^(4*x) + 6*x^2 + 9) + 2*log(x))

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mupad [B]  time = 1.56, size = 45, normalized size = 1.61 \begin {gather*} \frac {2}{\ln \left (\frac {{\mathrm {e}}^{-4\,x}\,\left ({\mathrm {e}}^{4\,x}\,\left (2\,x^2\,\ln \relax (2)-6\,x^2\right )+6\,x^2+x^4+9\right )}{x^2}\right )}-x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((72*x + 48*x^3 - 4*x^4 + 8*x^5 - log((exp(-4*x)*(exp(4*x)*(2*x^2*log(2) - 6*x^2) + 6*x^2 + x^4 + 9))/x^2)^
2*(9*x + exp(4*x)*(2*x^3*log(2) - 6*x^3) + 6*x^3 + x^5) + 36)/(log((exp(-4*x)*(exp(4*x)*(2*x^2*log(2) - 6*x^2)
+ 6*x^2 + x^4 + 9))/x^2)^2*(9*x + exp(4*x)*(2*x^3*log(2) - 6*x^3) + 6*x^3 + x^5)),x)

[Out]

2/log((exp(-4*x)*(exp(4*x)*(2*x^2*log(2) - 6*x^2) + 6*x^2 + x^4 + 9))/x^2) - x

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sympy [A]  time = 0.56, size = 41, normalized size = 1.46 \begin {gather*} - x + \frac {2}{\log {\left (\frac {\left (x^{4} + 6 x^{2} + \left (- 6 x^{2} + 2 x^{2} \log {\relax (2 )}\right ) e^{4 x} + 9\right ) e^{- 4 x}}{x^{2}} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x**3*ln(2)+6*x**3)*exp(x)**4-x**5-6*x**3-9*x)*ln(((2*x**2*ln(2)-6*x**2)*exp(x)**4+x**4+6*x**2+
9)/x**2/exp(x)**4)**2+8*x**5-4*x**4+48*x**3+72*x+36)/((2*x**3*ln(2)-6*x**3)*exp(x)**4+x**5+6*x**3+9*x)/ln(((2*
x**2*ln(2)-6*x**2)*exp(x)**4+x**4+6*x**2+9)/x**2/exp(x)**4)**2,x)

[Out]

-x + 2/log((x**4 + 6*x**2 + (-6*x**2 + 2*x**2*log(2))*exp(4*x) + 9)*exp(-4*x)/x**2)

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