3.82.89 \(\int \frac {-200+e^x (-8-2 x)-144 x+8 x^2+(8+8 x) \log (2)+(52 x+2 e^x x) \log (e^{2 x} x^2)+18 x \log ^2(e^{2 x} x^2)+2 x \log ^3(e^{2 x} x^2)}{27 x+27 x \log (e^{2 x} x^2)+9 x \log ^2(e^{2 x} x^2)+x \log ^3(e^{2 x} x^2)} \, dx\)

Optimal. Leaf size=30 \[ 2 \left (x-\frac {-25-e^x+x+\log (2)}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2}\right ) \]

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Rubi [F]  time = 1.61, 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 {-200+e^x (-8-2 x)-144 x+8 x^2+(8+8 x) \log (2)+\left (52 x+2 e^x x\right ) \log \left (e^{2 x} x^2\right )+18 x \log ^2\left (e^{2 x} x^2\right )+2 x \log ^3\left (e^{2 x} x^2\right )}{27 x+27 x \log \left (e^{2 x} x^2\right )+9 x \log ^2\left (e^{2 x} x^2\right )+x \log ^3\left (e^{2 x} x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-200 + E^x*(-8 - 2*x) - 144*x + 8*x^2 + (8 + 8*x)*Log[2] + (52*x + 2*E^x*x)*Log[E^(2*x)*x^2] + 18*x*Log[E
^(2*x)*x^2]^2 + 2*x*Log[E^(2*x)*x^2]^3)/(27*x + 27*x*Log[E^(2*x)*x^2] + 9*x*Log[E^(2*x)*x^2]^2 + x*Log[E^(2*x)
*x^2]^3),x]

[Out]

2*x - (2*Log[2])/(3 + Log[E^(2*x)*x^2])^2 - 192*Defer[Int][(3 + Log[E^(2*x)*x^2])^(-3), x] - 8*Defer[Int][E^x/
(3 + Log[E^(2*x)*x^2])^3, x] - 200*Defer[Int][1/(x*(3 + Log[E^(2*x)*x^2])^3), x] - 8*Defer[Int][E^x/(x*(3 + Lo
g[E^(2*x)*x^2])^3), x] + 8*Defer[Int][x/(3 + Log[E^(2*x)*x^2])^3, x] - 2*Defer[Int][(3 + Log[E^(2*x)*x^2])^(-2
), x] + 2*Defer[Int][E^x/(3 + Log[E^(2*x)*x^2])^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-200+e^x (-8-2 x)-144 x+8 x^2+(8+8 x) \log (2)+\left (52 x+2 e^x x\right ) \log \left (e^{2 x} x^2\right )+18 x \log ^2\left (e^{2 x} x^2\right )+2 x \log ^3\left (e^{2 x} x^2\right )}{x \left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx\\ &=\int \left (-\frac {144}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3}-\frac {200}{x \left (3+\log \left (e^{2 x} x^2\right )\right )^3}+\frac {8 x}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3}+\frac {8 (1+x) \log (2)}{x \left (3+\log \left (e^{2 x} x^2\right )\right )^3}+\frac {52 \log \left (e^{2 x} x^2\right )}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3}+\frac {18 \log ^2\left (e^{2 x} x^2\right )}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3}+\frac {2 \log ^3\left (e^{2 x} x^2\right )}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3}+\frac {2 e^x \left (-4-x+x \log \left (e^{2 x} x^2\right )\right )}{x \left (3+\log \left (e^{2 x} x^2\right )\right )^3}\right ) \, dx\\ &=2 \int \frac {\log ^3\left (e^{2 x} x^2\right )}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx+2 \int \frac {e^x \left (-4-x+x \log \left (e^{2 x} x^2\right )\right )}{x \left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx+8 \int \frac {x}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx+18 \int \frac {\log ^2\left (e^{2 x} x^2\right )}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx+52 \int \frac {\log \left (e^{2 x} x^2\right )}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx-144 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx-200 \int \frac {1}{x \left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx+(8 \log (2)) \int \frac {1+x}{x \left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx\\ &=-\frac {2 \log (2)}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2}+2 \int \left (-\frac {4 e^x (1+x)}{x \left (3+\log \left (e^{2 x} x^2\right )\right )^3}+\frac {e^x}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2}\right ) \, dx+2 \int \left (1-\frac {27}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3}+\frac {27}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2}-\frac {9}{3+\log \left (e^{2 x} x^2\right )}\right ) \, dx+8 \int \frac {x}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx+18 \int \left (\frac {9}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3}-\frac {6}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2}+\frac {1}{3+\log \left (e^{2 x} x^2\right )}\right ) \, dx+52 \int \left (-\frac {3}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3}+\frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2}\right ) \, dx-144 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx-200 \int \frac {1}{x \left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx\\ &=2 x-\frac {2 \log (2)}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2}+2 \int \frac {e^x}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2} \, dx+8 \int \frac {x}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx-8 \int \frac {e^x (1+x)}{x \left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx+52 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2} \, dx-54 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx+54 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2} \, dx-108 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2} \, dx-144 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx-156 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx+162 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx-200 \int \frac {1}{x \left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx\\ &=2 x-\frac {2 \log (2)}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2}+2 \int \frac {e^x}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2} \, dx+8 \int \frac {x}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx-8 \int \left (\frac {e^x}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3}+\frac {e^x}{x \left (3+\log \left (e^{2 x} x^2\right )\right )^3}\right ) \, dx+52 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2} \, dx-54 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx+54 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2} \, dx-108 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2} \, dx-144 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx-156 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx+162 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx-200 \int \frac {1}{x \left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx\\ &=2 x-\frac {2 \log (2)}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2}+2 \int \frac {e^x}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2} \, dx-8 \int \frac {e^x}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx-8 \int \frac {e^x}{x \left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx+8 \int \frac {x}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx+52 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2} \, dx-54 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx+54 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2} \, dx-108 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^2} \, dx-144 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx-156 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx+162 \int \frac {1}{\left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx-200 \int \frac {1}{x \left (3+\log \left (e^{2 x} x^2\right )\right )^3} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.07, size = 36, normalized size = 1.20 \begin {gather*} 2 \left (x+\frac {100+4 e^x-4 x-\log (16)}{4 \left (3+\log \left (e^{2 x} x^2\right )\right )^2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-200 + E^x*(-8 - 2*x) - 144*x + 8*x^2 + (8 + 8*x)*Log[2] + (52*x + 2*E^x*x)*Log[E^(2*x)*x^2] + 18*x
*Log[E^(2*x)*x^2]^2 + 2*x*Log[E^(2*x)*x^2]^3)/(27*x + 27*x*Log[E^(2*x)*x^2] + 9*x*Log[E^(2*x)*x^2]^2 + x*Log[E
^(2*x)*x^2]^3),x]

[Out]

2*(x + (100 + 4*E^x - 4*x - Log[16])/(4*(3 + Log[E^(2*x)*x^2])^2))

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fricas [B]  time = 1.12, size = 64, normalized size = 2.13 \begin {gather*} \frac {2 \, {\left (x \log \left (x^{2} e^{\left (2 \, x\right )}\right )^{2} + 6 \, x \log \left (x^{2} e^{\left (2 \, x\right )}\right ) + 8 \, x + e^{x} - \log \relax (2) + 25\right )}}{\log \left (x^{2} e^{\left (2 \, x\right )}\right )^{2} + 6 \, \log \left (x^{2} e^{\left (2 \, x\right )}\right ) + 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*log(exp(x)^2*x^2)^3+18*x*log(exp(x)^2*x^2)^2+(2*exp(x)*x+52*x)*log(exp(x)^2*x^2)+(-2*x-8)*exp(x
)+(8*x+8)*log(2)+8*x^2-144*x-200)/(x*log(exp(x)^2*x^2)^3+9*x*log(exp(x)^2*x^2)^2+27*x*log(exp(x)^2*x^2)+27*x),
x, algorithm="fricas")

[Out]

2*(x*log(x^2*e^(2*x))^2 + 6*x*log(x^2*e^(2*x)) + 8*x + e^x - log(2) + 25)/(log(x^2*e^(2*x))^2 + 6*log(x^2*e^(2
*x)) + 9)

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giac [B]  time = 0.52, size = 78, normalized size = 2.60 \begin {gather*} \frac {2 \, {\left (4 \, x^{3} + 4 \, x^{2} \log \left (x^{2}\right ) + x \log \left (x^{2}\right )^{2} + 12 \, x^{2} + 6 \, x \log \left (x^{2}\right ) + 8 \, x + e^{x} - \log \relax (2) + 25\right )}}{4 \, x^{2} + 4 \, x \log \left (x^{2}\right ) + \log \left (x^{2}\right )^{2} + 12 \, x + 6 \, \log \left (x^{2}\right ) + 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*log(exp(x)^2*x^2)^3+18*x*log(exp(x)^2*x^2)^2+(2*exp(x)*x+52*x)*log(exp(x)^2*x^2)+(-2*x-8)*exp(x
)+(8*x+8)*log(2)+8*x^2-144*x-200)/(x*log(exp(x)^2*x^2)^3+9*x*log(exp(x)^2*x^2)^2+27*x*log(exp(x)^2*x^2)+27*x),
x, algorithm="giac")

[Out]

2*(4*x^3 + 4*x^2*log(x^2) + x*log(x^2)^2 + 12*x^2 + 6*x*log(x^2) + 8*x + e^x - log(2) + 25)/(4*x^2 + 4*x*log(x
^2) + log(x^2)^2 + 12*x + 6*log(x^2) + 9)

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maple [C]  time = 2.12, size = 215, normalized size = 7.17

method	result	size
risch	\(2 x +\frac {8 \ln \relax (2)-8 \,{\mathrm e}^{x}-200+8 x}{\left (\pi \mathrm {csgn}\left (i x^{2} {\mathrm e}^{2 x}\right )^{3}-\pi \mathrm {csgn}\left (i x^{2} {\mathrm e}^{2 x}\right )^{2} \mathrm {csgn}\left (i x^{2}\right )-\pi \mathrm {csgn}\left (i x^{2} {\mathrm e}^{2 x}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right )+\pi \,\mathrm {csgn}\left (i x^{2} {\mathrm e}^{2 x}\right ) \mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right )+\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}+\pi \mathrm {csgn}\left (i {\mathrm e}^{x}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right )-2 \pi \,\mathrm {csgn}\left (i {\mathrm e}^{x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right )^{2}+\pi \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right )^{3}+4 i \ln \relax (x )+4 i \ln \left ({\mathrm e}^{x}\right )+6 i\right )^{2}}\)	\(215\)
default	\(\frac {2 \left (-4 \ln \left ({\mathrm e}^{2 x} x^{2}\right )+8 \ln \relax (x )+8 x -12\right ) \ln \relax (x )^{2}+2 \left (-3 \left (\ln \left ({\mathrm e}^{2 x} x^{2}\right )-2 \ln \left ({\mathrm e}^{x}\right )-2 \ln \relax (x )\right )^{2}-12 \left (\ln \left ({\mathrm e}^{x}\right )-x \right ) \left (\ln \left ({\mathrm e}^{2 x} x^{2}\right )-2 \ln \left ({\mathrm e}^{x}\right )-2 \ln \relax (x )\right )-12 \left (\ln \left ({\mathrm e}^{x}\right )-x \right )^{2}-18 \ln \left ({\mathrm e}^{2 x} x^{2}\right )+36 \ln \relax (x )+36 x -28\right ) x +2 \left (-4 \left (\ln \left ({\mathrm e}^{2 x} x^{2}\right )-2 \ln \left ({\mathrm e}^{x}\right )-2 \ln \relax (x )\right )^{2}-16 \left (\ln \left ({\mathrm e}^{x}\right )-x \right ) \left (\ln \left ({\mathrm e}^{2 x} x^{2}\right )-2 \ln \left ({\mathrm e}^{x}\right )-2 \ln \relax (x )\right )-16 \left (\ln \left ({\mathrm e}^{x}\right )-x \right )^{2}-24 \ln \left ({\mathrm e}^{2 x} x^{2}\right )+48 \ln \relax (x )+48 x -36\right ) \ln \relax (x )+8 x \ln \relax (x )^{2}+16 x^{2} \ln \relax (x )+2 \left (-4 \ln \left ({\mathrm e}^{2 x} x^{2}\right )+8 \ln \relax (x )+8 x -12\right ) x \ln \relax (x )+8 x^{3}-4-2 \left (\ln \left ({\mathrm e}^{2 x} x^{2}\right )-2 \ln \left ({\mathrm e}^{x}\right )-2 \ln \relax (x )\right )^{3}-12 \left (\ln \left ({\mathrm e}^{2 x} x^{2}\right )-2 \ln \left ({\mathrm e}^{x}\right )-2 \ln \relax (x )\right )^{2} \left (\ln \left ({\mathrm e}^{x}\right )-x \right )-24 \left (\ln \left ({\mathrm e}^{2 x} x^{2}\right )-2 \ln \left ({\mathrm e}^{x}\right )-2 \ln \relax (x )\right ) \left (\ln \left ({\mathrm e}^{x}\right )-x \right )^{2}-16 \left (\ln \left ({\mathrm e}^{x}\right )-x \right )^{3}-18 \left (\ln \left ({\mathrm e}^{2 x} x^{2}\right )-2 \ln \left ({\mathrm e}^{x}\right )-2 \ln \relax (x )\right )^{2}-72 \left (\ln \left ({\mathrm e}^{x}\right )-x \right ) \left (\ln \left ({\mathrm e}^{2 x} x^{2}\right )-2 \ln \left ({\mathrm e}^{x}\right )-2 \ln \relax (x )\right )-72 \left (\ln \left ({\mathrm e}^{x}\right )-x \right )^{2}-54 \ln \left ({\mathrm e}^{2 x} x^{2}\right )+108 \ln \relax (x )+108 x}{\left (3+\ln \left ({\mathrm e}^{2 x} x^{2}\right )\right )^{2}}-\frac {2 \ln \relax (2)}{\left (3+\ln \left ({\mathrm e}^{2 x} x^{2}\right )\right )^{2}}+\frac {2 \,{\mathrm e}^{x}}{\left (3+\ln \left ({\mathrm e}^{2 x} x^{2}\right )\right )^{2}}\)	\(464\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x*ln(exp(x)^2*x^2)^3+18*x*ln(exp(x)^2*x^2)^2+(2*exp(x)*x+52*x)*ln(exp(x)^2*x^2)+(-2*x-8)*exp(x)+(8*x+8)
*ln(2)+8*x^2-144*x-200)/(x*ln(exp(x)^2*x^2)^3+9*x*ln(exp(x)^2*x^2)^2+27*x*ln(exp(x)^2*x^2)+27*x),x,method=_RET
URNVERBOSE)

[Out]

2*x+8*(ln(2)-exp(x)-25+x)/(Pi*csgn(I*x^2*exp(2*x))^3-Pi*csgn(I*x^2*exp(2*x))^2*csgn(I*x^2)-Pi*csgn(I*x^2*exp(2
*x))^2*csgn(I*exp(2*x))+Pi*csgn(I*x^2*exp(2*x))*csgn(I*x^2)*csgn(I*exp(2*x))+Pi*csgn(I*x)^2*csgn(I*x^2)-2*Pi*c
sgn(I*x)*csgn(I*x^2)^2+Pi*csgn(I*x^2)^3+Pi*csgn(I*exp(x))^2*csgn(I*exp(2*x))-2*Pi*csgn(I*exp(x))*csgn(I*exp(2*
x))^2+Pi*csgn(I*exp(2*x))^3+4*I*ln(x)+4*I*ln(exp(x))+6*I)^2

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maxima [B]  time = 0.51, size = 70, normalized size = 2.33 \begin {gather*} \frac {2 \, {\left (4 \, x^{3} + 4 \, x \log \relax (x)^{2} + 12 \, x^{2} + 4 \, {\left (2 \, x^{2} + 3 \, x\right )} \log \relax (x) + 8 \, x + e^{x} - \log \relax (2) + 25\right )}}{4 \, x^{2} + 4 \, {\left (2 \, x + 3\right )} \log \relax (x) + 4 \, \log \relax (x)^{2} + 12 \, x + 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*log(exp(x)^2*x^2)^3+18*x*log(exp(x)^2*x^2)^2+(2*exp(x)*x+52*x)*log(exp(x)^2*x^2)+(-2*x-8)*exp(x
)+(8*x+8)*log(2)+8*x^2-144*x-200)/(x*log(exp(x)^2*x^2)^3+9*x*log(exp(x)^2*x^2)^2+27*x*log(exp(x)^2*x^2)+27*x),
x, algorithm="maxima")

[Out]

2*(4*x^3 + 4*x*log(x)^2 + 12*x^2 + 4*(2*x^2 + 3*x)*log(x) + 8*x + e^x - log(2) + 25)/(4*x^2 + 4*(2*x + 3)*log(
x) + 4*log(x)^2 + 12*x + 9)

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mupad [B]  time = 5.50, size = 30, normalized size = 1.00 \begin {gather*} 2\,x-\frac {2\,x+\ln \relax (4)-2\,{\mathrm {e}}^x-50}{{\left (\ln \left (x^2\,{\mathrm {e}}^{2\,x}\right )+3\right )}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(2)*(8*x + 8) - 144*x + 18*x*log(x^2*exp(2*x))^2 + 2*x*log(x^2*exp(2*x))^3 + log(x^2*exp(2*x))*(52*x +
2*x*exp(x)) - exp(x)*(2*x + 8) + 8*x^2 - 200)/(27*x + 9*x*log(x^2*exp(2*x))^2 + x*log(x^2*exp(2*x))^3 + 27*x*
log(x^2*exp(2*x))),x)

[Out]

2*x - (2*x + log(4) - 2*exp(x) - 50)/(log(x^2*exp(2*x)) + 3)^2

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sympy [A]  time = 0.35, size = 42, normalized size = 1.40 \begin {gather*} 2 x + \frac {- 2 x + 2 e^{x} - 2 \log {\relax (2 )} + 50}{\log {\left (x^{2} e^{2 x} \right )}^{2} + 6 \log {\left (x^{2} e^{2 x} \right )} + 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*ln(exp(x)**2*x**2)**3+18*x*ln(exp(x)**2*x**2)**2+(2*exp(x)*x+52*x)*ln(exp(x)**2*x**2)+(-2*x-8)*
exp(x)+(8*x+8)*ln(2)+8*x**2-144*x-200)/(x*ln(exp(x)**2*x**2)**3+9*x*ln(exp(x)**2*x**2)**2+27*x*ln(exp(x)**2*x*
*2)+27*x),x)

[Out]

2*x + (-2*x + 2*exp(x) - 2*log(2) + 50)/(log(x**2*exp(2*x))**2 + 6*log(x**2*exp(2*x)) + 9)

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