3.43.77 \(\int \frac {-8-e^4+x^2-\log (x)+(9+e^4+8 x+x^2+\log (x)) \log (\frac {x}{9+e^4+8 x+x^2+\log (x)})+(9+e^4+8 x+x^2+e^x (-9-e^4-8 x-x^2)+(1-e^x) \log (x)) \log ^2(\frac {x}{9+e^4+8 x+x^2+\log (x)})}{(9+e^4+8 x+x^2+\log (x)) \log ^2(\frac {x}{9+e^4+8 x+x^2+\log (x)})} \, dx\)

Optimal. Leaf size=30 \[ -e^x+x+\frac {x}{\log \left (\frac {x}{e^4+2 x+(3+x)^2+\log (x)}\right )} \]

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Rubi [F]  time = 2.63, 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 {-8-e^4+x^2-\log (x)+\left (9+e^4+8 x+x^2+\log (x)\right ) \log \left (\frac {x}{9+e^4+8 x+x^2+\log (x)}\right )+\left (9+e^4+8 x+x^2+e^x \left (-9-e^4-8 x-x^2\right )+\left (1-e^x\right ) \log (x)\right ) \log ^2\left (\frac {x}{9+e^4+8 x+x^2+\log (x)}\right )}{\left (9+e^4+8 x+x^2+\log (x)\right ) \log ^2\left (\frac {x}{9+e^4+8 x+x^2+\log (x)}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-8 - E^4 + x^2 - Log[x] + (9 + E^4 + 8*x + x^2 + Log[x])*Log[x/(9 + E^4 + 8*x + x^2 + Log[x])] + (9 + E^4
+ 8*x + x^2 + E^x*(-9 - E^4 - 8*x - x^2) + (1 - E^x)*Log[x])*Log[x/(9 + E^4 + 8*x + x^2 + Log[x])]^2)/((9 + E
^4 + 8*x + x^2 + Log[x])*Log[x/(9 + E^4 + 8*x + x^2 + Log[x])]^2),x]

[Out]

-E^x + x + (9 + E^4)*Defer[Int][(-9*(1 + E^4/9) - 8*x - x^2 - Log[x])^(-1), x] + 8*Defer[Int][x/(-9*(1 + E^4/9
) - 8*x - x^2 - Log[x]), x] + Defer[Int][x^2/(-9*(1 + E^4/9) - 8*x - x^2 - Log[x]), x] + (9 + E^4)*Defer[Int][
(9*(1 + E^4/9) + 8*x + x^2 + Log[x])^(-1), x] + 8*Defer[Int][x/(9*(1 + E^4/9) + 8*x + x^2 + Log[x]), x] + Defe
r[Int][x^2/(9*(1 + E^4/9) + 8*x + x^2 + Log[x]), x] + Defer[Int][Log[x]/((-9*(1 + E^4/9) - 8*x - x^2 - Log[x])
*Log[x/(9*(1 + E^4/9) + 8*x + x^2 + Log[x])]^2), x] - (8 + E^4)*Defer[Int][1/((9*(1 + E^4/9) + 8*x + x^2 + Log
[x])*Log[x/(9*(1 + E^4/9) + 8*x + x^2 + Log[x])]^2), x] + Defer[Int][x^2/((9*(1 + E^4/9) + 8*x + x^2 + Log[x])
*Log[x/(9*(1 + E^4/9) + 8*x + x^2 + Log[x])]^2), x] + Defer[Int][Log[x/(9*(1 + E^4/9) + 8*x + x^2 + Log[x])]^(
-1), x]

Rubi steps

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

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Mathematica [A]  time = 0.14, size = 29, normalized size = 0.97 \begin {gather*} -e^x+x+\frac {x}{\log \left (\frac {x}{9+e^4+8 x+x^2+\log (x)}\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-8 - E^4 + x^2 - Log[x] + (9 + E^4 + 8*x + x^2 + Log[x])*Log[x/(9 + E^4 + 8*x + x^2 + Log[x])] + (9
+ E^4 + 8*x + x^2 + E^x*(-9 - E^4 - 8*x - x^2) + (1 - E^x)*Log[x])*Log[x/(9 + E^4 + 8*x + x^2 + Log[x])]^2)/(
(9 + E^4 + 8*x + x^2 + Log[x])*Log[x/(9 + E^4 + 8*x + x^2 + Log[x])]^2),x]

[Out]

-E^x + x + x/Log[x/(9 + E^4 + 8*x + x^2 + Log[x])]

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fricas [A]  time = 0.56, size = 46, normalized size = 1.53 \begin {gather*} \frac {{\left (x - e^{x}\right )} \log \left (\frac {x}{x^{2} + 8 \, x + e^{4} + \log \relax (x) + 9}\right ) + x}{\log \left (\frac {x}{x^{2} + 8 \, x + e^{4} + \log \relax (x) + 9}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((1-exp(x))*log(x)+(-exp(4)-x^2-8*x-9)*exp(x)+exp(4)+x^2+8*x+9)*log(x/(log(x)+exp(4)+x^2+8*x+9))^2+
(log(x)+exp(4)+x^2+8*x+9)*log(x/(log(x)+exp(4)+x^2+8*x+9))-log(x)-exp(4)+x^2-8)/(log(x)+exp(4)+x^2+8*x+9)/log(
x/(log(x)+exp(4)+x^2+8*x+9))^2,x, algorithm="fricas")

[Out]

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

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giac [B]  time = 0.53, size = 67, normalized size = 2.23 \begin {gather*} \frac {x \log \left (x^{2} + 8 \, x + e^{4} + \log \relax (x) + 9\right ) - e^{x} \log \left (x^{2} + 8 \, x + e^{4} + \log \relax (x) + 9\right ) - x \log \relax (x) + e^{x} \log \relax (x) - x}{\log \left (x^{2} + 8 \, x + e^{4} + \log \relax (x) + 9\right ) - \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((1-exp(x))*log(x)+(-exp(4)-x^2-8*x-9)*exp(x)+exp(4)+x^2+8*x+9)*log(x/(log(x)+exp(4)+x^2+8*x+9))^2+
(log(x)+exp(4)+x^2+8*x+9)*log(x/(log(x)+exp(4)+x^2+8*x+9))-log(x)-exp(4)+x^2-8)/(log(x)+exp(4)+x^2+8*x+9)/log(
x/(log(x)+exp(4)+x^2+8*x+9))^2,x, algorithm="giac")

[Out]

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

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maple [C]  time = 0.22, size = 173, normalized size = 5.77

method	result	size
risch	\(x -{\mathrm e}^{x}+\frac {2 i x}{\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i}{\ln \relax (x )+{\mathrm e}^{4}+x^{2}+8 x +9}\right ) \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )+{\mathrm e}^{4}+x^{2}+8 x +9}\right )-\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )+{\mathrm e}^{4}+x^{2}+8 x +9}\right )^{2}-\pi \,\mathrm {csgn}\left (\frac {i}{\ln \relax (x )+{\mathrm e}^{4}+x^{2}+8 x +9}\right ) \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )+{\mathrm e}^{4}+x^{2}+8 x +9}\right )^{2}+\pi \mathrm {csgn}\left (\frac {i x}{\ln \relax (x )+{\mathrm e}^{4}+x^{2}+8 x +9}\right )^{3}+2 i \ln \relax (x )-2 i \ln \left (\ln \relax (x )+{\mathrm e}^{4}+x^{2}+8 x +9\right )}\)	\(173\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((1-exp(x))*ln(x)+(-exp(4)-x^2-8*x-9)*exp(x)+exp(4)+x^2+8*x+9)*ln(x/(ln(x)+exp(4)+x^2+8*x+9))^2+(ln(x)+ex
p(4)+x^2+8*x+9)*ln(x/(ln(x)+exp(4)+x^2+8*x+9))-ln(x)-exp(4)+x^2-8)/(ln(x)+exp(4)+x^2+8*x+9)/ln(x/(ln(x)+exp(4)
+x^2+8*x+9))^2,x,method=_RETURNVERBOSE)

[Out]

x-exp(x)+2*I*x/(Pi*csgn(I*x)*csgn(I/(ln(x)+exp(4)+x^2+8*x+9))*csgn(I*x/(ln(x)+exp(4)+x^2+8*x+9))-Pi*csgn(I*x)*
csgn(I*x/(ln(x)+exp(4)+x^2+8*x+9))^2-Pi*csgn(I/(ln(x)+exp(4)+x^2+8*x+9))*csgn(I*x/(ln(x)+exp(4)+x^2+8*x+9))^2+
Pi*csgn(I*x/(ln(x)+exp(4)+x^2+8*x+9))^3+2*I*ln(x)-2*I*ln(ln(x)+exp(4)+x^2+8*x+9))

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maxima [A]  time = 0.39, size = 55, normalized size = 1.83 \begin {gather*} \frac {{\left (x - e^{x}\right )} \log \left (x^{2} + 8 \, x + e^{4} + \log \relax (x) + 9\right ) - x \log \relax (x) + e^{x} \log \relax (x) - x}{\log \left (x^{2} + 8 \, x + e^{4} + \log \relax (x) + 9\right ) - \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((1-exp(x))*log(x)+(-exp(4)-x^2-8*x-9)*exp(x)+exp(4)+x^2+8*x+9)*log(x/(log(x)+exp(4)+x^2+8*x+9))^2+
(log(x)+exp(4)+x^2+8*x+9)*log(x/(log(x)+exp(4)+x^2+8*x+9))-log(x)-exp(4)+x^2-8)/(log(x)+exp(4)+x^2+8*x+9)/log(
x/(log(x)+exp(4)+x^2+8*x+9))^2,x, algorithm="maxima")

[Out]

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

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mupad [B]  time = 3.61, size = 167, normalized size = 5.57 \begin {gather*} \frac {\frac {x\,\left (120\,x+{\mathrm {e}}^4+16\,x\,{\mathrm {e}}^4+6\,x^2\,{\mathrm {e}}^4+47\,x^2-2\,x^4+7\right )}{2\,x^2-1}+\frac {x\,\ln \relax (x)\,\left (6\,x^2+16\,x+1\right )}{2\,x^2-1}}{{\mathrm {e}}^4+\ln \relax (x)-x^2+8}-{\mathrm {e}}^x-\frac {2\,x+4}{x^2-\frac {1}{2}}-x+\frac {x-\frac {x\,\ln \left (\frac {x}{8\,x+{\mathrm {e}}^4+\ln \relax (x)+x^2+9}\right )\,\left (8\,x+{\mathrm {e}}^4+\ln \relax (x)+x^2+9\right )}{{\mathrm {e}}^4+\ln \relax (x)-x^2+8}}{\ln \left (\frac {x}{8\,x+{\mathrm {e}}^4+\ln \relax (x)+x^2+9}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(4) + log(x) - log(x/(8*x + exp(4) + log(x) + x^2 + 9))^2*(8*x + exp(4) - log(x)*(exp(x) - 1) - exp(x
)*(8*x + exp(4) + x^2 + 9) + x^2 + 9) - log(x/(8*x + exp(4) + log(x) + x^2 + 9))*(8*x + exp(4) + log(x) + x^2
+ 9) - x^2 + 8)/(log(x/(8*x + exp(4) + log(x) + x^2 + 9))^2*(8*x + exp(4) + log(x) + x^2 + 9)),x)

[Out]

((x*(120*x + exp(4) + 16*x*exp(4) + 6*x^2*exp(4) + 47*x^2 - 2*x^4 + 7))/(2*x^2 - 1) + (x*log(x)*(16*x + 6*x^2
+ 1))/(2*x^2 - 1))/(exp(4) + log(x) - x^2 + 8) - exp(x) - (2*x + 4)/(x^2 - 1/2) - x + (x - (x*log(x/(8*x + exp
(4) + log(x) + x^2 + 9))*(8*x + exp(4) + log(x) + x^2 + 9))/(exp(4) + log(x) - x^2 + 8))/log(x/(8*x + exp(4) +
log(x) + x^2 + 9))

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sympy [A]  time = 0.98, size = 24, normalized size = 0.80 \begin {gather*} x + \frac {x}{\log {\left (\frac {x}{x^{2} + 8 x + \log {\relax (x )} + 9 + e^{4}} \right )}} - e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((1-exp(x))*ln(x)+(-exp(4)-x**2-8*x-9)*exp(x)+exp(4)+x**2+8*x+9)*ln(x/(ln(x)+exp(4)+x**2+8*x+9))**2
+(ln(x)+exp(4)+x**2+8*x+9)*ln(x/(ln(x)+exp(4)+x**2+8*x+9))-ln(x)-exp(4)+x**2-8)/(ln(x)+exp(4)+x**2+8*x+9)/ln(x
/(ln(x)+exp(4)+x**2+8*x+9))**2,x)

[Out]

x + x/log(x/(x**2 + 8*x + log(x) + 9 + exp(4))) - exp(x)

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