3.19.66 \(\int \frac {64+208 x+33 x^2+2 x^3+(-16-50 x-4 x^2) \log (5)+(1+3 x) \log ^2(5)+e^x (-80-266 x-70 x^2-10 x^3-x^4+(26+82 x+10 x^2+x^3) \log (5)+(-2-6 x) \log ^2(5))+e^{2 x} (25+85 x+31 x^2+3 x^3+(-10-32 x-6 x^2) \log (5)+(1+3 x) \log ^2(5))}{64 x+16 x^2+x^3+(-16 x-2 x^2) \log (5)+x \log ^2(5)+e^x (-80 x-26 x^2-2 x^3+(26 x+4 x^2) \log (5)-2 x \log ^2(5))+e^{2 x} (25 x+10 x^2+x^3+(-10 x-2 x^2) \log (5)+x \log ^2(5))} \, dx\)

Optimal. Leaf size=32 \[ 3 x+\frac {x}{-\frac {3}{x}+\frac {\left (-1+e^x\right ) (5+x-\log (5))}{x}}+\log (x) \]

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Rubi [F]  time = 7.07, 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 {64+208 x+33 x^2+2 x^3+\left (-16-50 x-4 x^2\right ) \log (5)+(1+3 x) \log ^2(5)+e^x \left (-80-266 x-70 x^2-10 x^3-x^4+\left (26+82 x+10 x^2+x^3\right ) \log (5)+(-2-6 x) \log ^2(5)\right )+e^{2 x} \left (25+85 x+31 x^2+3 x^3+\left (-10-32 x-6 x^2\right ) \log (5)+(1+3 x) \log ^2(5)\right )}{64 x+16 x^2+x^3+\left (-16 x-2 x^2\right ) \log (5)+x \log ^2(5)+e^x \left (-80 x-26 x^2-2 x^3+\left (26 x+4 x^2\right ) \log (5)-2 x \log ^2(5)\right )+e^{2 x} \left (25 x+10 x^2+x^3+\left (-10 x-2 x^2\right ) \log (5)+x \log ^2(5)\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(64 + 208*x + 33*x^2 + 2*x^3 + (-16 - 50*x - 4*x^2)*Log[5] + (1 + 3*x)*Log[5]^2 + E^x*(-80 - 266*x - 70*x^
2 - 10*x^3 - x^4 + (26 + 82*x + 10*x^2 + x^3)*Log[5] + (-2 - 6*x)*Log[5]^2) + E^(2*x)*(25 + 85*x + 31*x^2 + 3*
x^3 + (-10 - 32*x - 6*x^2)*Log[5] + (1 + 3*x)*Log[5]^2))/(64*x + 16*x^2 + x^3 + (-16*x - 2*x^2)*Log[5] + x*Log
[5]^2 + E^x*(-80*x - 26*x^2 - 2*x^3 + (26*x + 4*x^2)*Log[5] - 2*x*Log[5]^2) + E^(2*x)*(25*x + 10*x^2 + x^3 + (
-10*x - 2*x^2)*Log[5] + x*Log[5]^2)),x]

[Out]

3*x + Log[x] + (5 - Log[5])*Defer[Int][(-x + E^x*x + 5*E^x*(1 - Log[5]/5) - 8*(1 - Log[5]/8))^(-1), x] + Defer
[Int][x/(-x + E^x*x + 5*E^x*(1 - Log[5]/5) - 8*(1 - Log[5]/8)), x] + (5 - Log[5])*(3 + 2*Log[5]^2 - Log[5]*Log
[25])*Defer[Int][(x - E^x*x - 5*E^x*(1 - Log[5]/5) + 8*(1 - Log[5]/8))^(-2), x] - (3 + 2*Log[5]^2 - Log[5]*Log
[25])*Defer[Int][x/(x - E^x*x - 5*E^x*(1 - Log[5]/5) + 8*(1 - Log[5]/8))^2, x] - (8 - Log[5])*Defer[Int][x^2/(
x - E^x*x - 5*E^x*(1 - Log[5]/5) + 8*(1 - Log[5]/8))^2, x] - Defer[Int][x^3/(x - E^x*x - 5*E^x*(1 - Log[5]/5)
+ 8*(1 - Log[5]/8))^2, x] + Defer[Int][x^2/(x - E^x*x - 5*E^x*(1 - Log[5]/5) + 8*(1 - Log[5]/8)), x] - (5 - Lo
g[5])^2*(3 + 2*Log[5]^2 - Log[5]*Log[25])*Defer[Int][1/((x - E^x*x - 5*E^x*(1 - Log[5]/5) + 8*(1 - Log[5]/8))^
2*(5 + x - Log[5])), x] + (5 - Log[5])^2*Defer[Int][1/((x - E^x*x - 5*E^x*(1 - Log[5]/5) + 8*(1 - Log[5]/8))*(
5 + x - Log[5])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {64+208 x+33 x^2+2 x^3+\left (-16-50 x-4 x^2\right ) \log (5)+(1+3 x) \log ^2(5)+e^x \left (-80-266 x-70 x^2-10 x^3-x^4+\left (26+82 x+10 x^2+x^3\right ) \log (5)+(-2-6 x) \log ^2(5)\right )+e^{2 x} \left (25+85 x+31 x^2+3 x^3+\left (-10-32 x-6 x^2\right ) \log (5)+(1+3 x) \log ^2(5)\right )}{16 x^2+x^3+\left (-16 x-2 x^2\right ) \log (5)+x \left (64+\log ^2(5)\right )+e^x \left (-80 x-26 x^2-2 x^3+\left (26 x+4 x^2\right ) \log (5)-2 x \log ^2(5)\right )+e^{2 x} \left (25 x+10 x^2+x^3+\left (-10 x-2 x^2\right ) \log (5)+x \log ^2(5)\right )} \, dx\\ &=\int \frac {2 x^3+x^2 (33-4 \log (5))+e^{2 x} (1+3 x) (5+x-\log (5))^2+(-8+\log (5))^2+x \left (208-50 \log (5)+3 \log ^2(5)\right )-e^x \left (x^4-x^3 (-10+\log (5))-10 x^2 (-7+\log (5))+2 \left (40-13 \log (5)+\log ^2(5)\right )+x \left (266-82 \log (5)+6 \log ^2(5)\right )\right )}{x \left (x-e^x (5+x-\log (5))+8 \left (1-\frac {\log (5)}{8}\right )\right )^2} \, dx\\ &=\int \left (\frac {1+3 x}{x}+\frac {x^2 \left (-43-x^2-x (13-2 \log (5))+13 \log (5)-\log ^2(5)\right )}{\left (x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )\right )^2 (5+x-\log (5))}+\frac {x \left (-10+x^2+x (4-\log (5))+\log (25)\right )}{\left (x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )\right ) (5+x-\log (5))}\right ) \, dx\\ &=\int \frac {1+3 x}{x} \, dx+\int \frac {x^2 \left (-43-x^2-x (13-2 \log (5))+13 \log (5)-\log ^2(5)\right )}{\left (x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )\right )^2 (5+x-\log (5))} \, dx+\int \frac {x \left (-10+x^2+x (4-\log (5))+\log (25)\right )}{\left (x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )\right ) (5+x-\log (5))} \, dx\\ &=\int \left (3+\frac {1}{x}\right ) \, dx+\int \left (\frac {x}{-x+e^x x+5 e^x \left (1-\frac {\log (5)}{5}\right )-8 \left (1-\frac {\log (5)}{8}\right )}+\frac {x^2}{x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )}+\frac {(5-\log (5))^2}{\left (x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )\right ) (5+x-\log (5))}+\frac {5 \left (1-\frac {\log (5)}{5}\right )}{-x+e^x x+5 e^x \left (1-\frac {\log (5)}{5}\right )-8 \left (1-\frac {\log (5)}{8}\right )}\right ) \, dx+\int \frac {x^2 \left (-43-x^2+13 \log (5)-\log ^2(5)-x (13-\log (25))\right )}{\left (x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )\right )^2 (5+x-\log (5))} \, dx\\ &=3 x+\log (x)+(5-\log (5)) \int \frac {1}{-x+e^x x+5 e^x \left (1-\frac {\log (5)}{5}\right )-8 \left (1-\frac {\log (5)}{8}\right )} \, dx+(5-\log (5))^2 \int \frac {1}{\left (x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )\right ) (5+x-\log (5))} \, dx+\int \frac {x}{-x+e^x x+5 e^x \left (1-\frac {\log (5)}{5}\right )-8 \left (1-\frac {\log (5)}{8}\right )} \, dx+\int \frac {x^2}{x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )} \, dx+\int \left (-\frac {x^3}{\left (x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )\right )^2}+\frac {x^2 (-8+\log (5))}{\left (x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )\right )^2}+\frac {(5-\log (5)) \left (3+2 \log ^2(5)-\log (5) \log (25)\right )}{\left (x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )\right )^2}+\frac {x \left (-3-2 \log ^2(5)+\log (5) \log (25)\right )}{\left (x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )\right )^2}+\frac {(5-\log (5))^2 \left (-3-2 \log ^2(5)+\log (5) \log (25)\right )}{\left (x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )\right )^2 (5+x-\log (5))}\right ) \, dx\\ &=3 x+\log (x)+(5-\log (5)) \int \frac {1}{-x+e^x x+5 e^x \left (1-\frac {\log (5)}{5}\right )-8 \left (1-\frac {\log (5)}{8}\right )} \, dx+(5-\log (5))^2 \int \frac {1}{\left (x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )\right ) (5+x-\log (5))} \, dx+(-8+\log (5)) \int \frac {x^2}{\left (x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )\right )^2} \, dx+\left ((5-\log (5)) \left (3+2 \log ^2(5)-\log (5) \log (25)\right )\right ) \int \frac {1}{\left (x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )\right )^2} \, dx-\left ((5-\log (5))^2 \left (3+2 \log ^2(5)-\log (5) \log (25)\right )\right ) \int \frac {1}{\left (x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )\right )^2 (5+x-\log (5))} \, dx+\left (-3-2 \log ^2(5)+\log (5) \log (25)\right ) \int \frac {x}{\left (x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )\right )^2} \, dx+\int \frac {x}{-x+e^x x+5 e^x \left (1-\frac {\log (5)}{5}\right )-8 \left (1-\frac {\log (5)}{8}\right )} \, dx-\int \frac {x^3}{\left (x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )\right )^2} \, dx+\int \frac {x^2}{x-e^x x-5 e^x \left (1-\frac {\log (5)}{5}\right )+8 \left (1-\frac {\log (5)}{8}\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.22, size = 29, normalized size = 0.91 \begin {gather*} x \left (3+\frac {x}{-8-x+e^x (5+x-\log (5))+\log (5)}\right )+\log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(64 + 208*x + 33*x^2 + 2*x^3 + (-16 - 50*x - 4*x^2)*Log[5] + (1 + 3*x)*Log[5]^2 + E^x*(-80 - 266*x -
70*x^2 - 10*x^3 - x^4 + (26 + 82*x + 10*x^2 + x^3)*Log[5] + (-2 - 6*x)*Log[5]^2) + E^(2*x)*(25 + 85*x + 31*x^
2 + 3*x^3 + (-10 - 32*x - 6*x^2)*Log[5] + (1 + 3*x)*Log[5]^2))/(64*x + 16*x^2 + x^3 + (-16*x - 2*x^2)*Log[5] +
x*Log[5]^2 + E^x*(-80*x - 26*x^2 - 2*x^3 + (26*x + 4*x^2)*Log[5] - 2*x*Log[5]^2) + E^(2*x)*(25*x + 10*x^2 + x
^3 + (-10*x - 2*x^2)*Log[5] + x*Log[5]^2)),x]

[Out]

x*(3 + x/(-8 - x + E^x*(5 + x - Log[5]) + Log[5])) + Log[x]

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fricas [B]  time = 0.79, size = 72, normalized size = 2.25 \begin {gather*} -\frac {2 \, x^{2} - 3 \, {\left (x^{2} - x \log \relax (5) + 5 \, x\right )} e^{x} - 3 \, x \log \relax (5) - {\left ({\left (x - \log \relax (5) + 5\right )} e^{x} - x + \log \relax (5) - 8\right )} \log \relax (x) + 24 \, x}{{\left (x - \log \relax (5) + 5\right )} e^{x} - x + \log \relax (5) - 8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3*x+1)*log(5)^2+(-6*x^2-32*x-10)*log(5)+3*x^3+31*x^2+85*x+25)*exp(x)^2+((-6*x-2)*log(5)^2+(x^3+10
*x^2+82*x+26)*log(5)-x^4-10*x^3-70*x^2-266*x-80)*exp(x)+(3*x+1)*log(5)^2+(-4*x^2-50*x-16)*log(5)+2*x^3+33*x^2+
208*x+64)/((x*log(5)^2+(-2*x^2-10*x)*log(5)+x^3+10*x^2+25*x)*exp(x)^2+(-2*x*log(5)^2+(4*x^2+26*x)*log(5)-2*x^3
-26*x^2-80*x)*exp(x)+x*log(5)^2+(-2*x^2-16*x)*log(5)+x^3+16*x^2+64*x),x, algorithm="fricas")

[Out]

-(2*x^2 - 3*(x^2 - x*log(5) + 5*x)*e^x - 3*x*log(5) - ((x - log(5) + 5)*e^x - x + log(5) - 8)*log(x) + 24*x)/(
(x - log(5) + 5)*e^x - x + log(5) - 8)

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giac [B]  time = 0.87, size = 91, normalized size = 2.84 \begin {gather*} \frac {3 \, x^{2} e^{x} - 3 \, x e^{x} \log \relax (5) + x e^{x} \log \relax (x) - e^{x} \log \relax (5) \log \relax (x) - 2 \, x^{2} + 15 \, x e^{x} + 3 \, x \log \relax (5) - x \log \relax (x) + 5 \, e^{x} \log \relax (x) + \log \relax (5) \log \relax (x) - 24 \, x - 8 \, \log \relax (x)}{x e^{x} - e^{x} \log \relax (5) - x + 5 \, e^{x} + \log \relax (5) - 8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3*x+1)*log(5)^2+(-6*x^2-32*x-10)*log(5)+3*x^3+31*x^2+85*x+25)*exp(x)^2+((-6*x-2)*log(5)^2+(x^3+10
*x^2+82*x+26)*log(5)-x^4-10*x^3-70*x^2-266*x-80)*exp(x)+(3*x+1)*log(5)^2+(-4*x^2-50*x-16)*log(5)+2*x^3+33*x^2+
208*x+64)/((x*log(5)^2+(-2*x^2-10*x)*log(5)+x^3+10*x^2+25*x)*exp(x)^2+(-2*x*log(5)^2+(4*x^2+26*x)*log(5)-2*x^3
-26*x^2-80*x)*exp(x)+x*log(5)^2+(-2*x^2-16*x)*log(5)+x^3+16*x^2+64*x),x, algorithm="giac")

[Out]

(3*x^2*e^x - 3*x*e^x*log(5) + x*e^x*log(x) - e^x*log(5)*log(x) - 2*x^2 + 15*x*e^x + 3*x*log(5) - x*log(x) + 5*
e^x*log(x) + log(5)*log(x) - 24*x - 8*log(x))/(x*e^x - e^x*log(5) - x + 5*e^x + log(5) - 8)

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maple [A]  time = 0.29, size = 35, normalized size = 1.09

method	result	size
risch	\(3 x +\ln \relax (x )-\frac {x^{2}}{{\mathrm e}^{x} \ln \relax (5)-{\mathrm e}^{x} x -5 \,{\mathrm e}^{x}-\ln \relax (5)+x +8}\)	\(35\)
norman	\(\frac {9 x +\left (3 \ln \relax (5)^{2}-30 \ln \relax (5)+75\right ) {\mathrm e}^{x}+2 x^{2}-3 \,{\mathrm e}^{x} x^{2}-3 \ln \relax (5)^{2}+39 \ln \relax (5)-120}{{\mathrm e}^{x} \ln \relax (5)-{\mathrm e}^{x} x -5 \,{\mathrm e}^{x}-\ln \relax (5)+x +8}+\ln \relax (x )\)	\(70\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((3*x+1)*ln(5)^2+(-6*x^2-32*x-10)*ln(5)+3*x^3+31*x^2+85*x+25)*exp(x)^2+((-6*x-2)*ln(5)^2+(x^3+10*x^2+82*x
+26)*ln(5)-x^4-10*x^3-70*x^2-266*x-80)*exp(x)+(3*x+1)*ln(5)^2+(-4*x^2-50*x-16)*ln(5)+2*x^3+33*x^2+208*x+64)/((
x*ln(5)^2+(-2*x^2-10*x)*ln(5)+x^3+10*x^2+25*x)*exp(x)^2+(-2*x*ln(5)^2+(4*x^2+26*x)*ln(5)-2*x^3-26*x^2-80*x)*ex
p(x)+x*ln(5)^2+(-2*x^2-16*x)*ln(5)+x^3+16*x^2+64*x),x,method=_RETURNVERBOSE)

[Out]

3*x+ln(x)-x^2/(exp(x)*ln(5)-exp(x)*x-5*exp(x)-ln(5)+x+8)

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maxima [A]  time = 0.86, size = 52, normalized size = 1.62 \begin {gather*} -\frac {2 \, x^{2} - 3 \, x {\left (\log \relax (5) - 8\right )} - 3 \, {\left (x^{2} - x {\left (\log \relax (5) - 5\right )}\right )} e^{x}}{{\left (x - \log \relax (5) + 5\right )} e^{x} - x + \log \relax (5) - 8} + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3*x+1)*log(5)^2+(-6*x^2-32*x-10)*log(5)+3*x^3+31*x^2+85*x+25)*exp(x)^2+((-6*x-2)*log(5)^2+(x^3+10
*x^2+82*x+26)*log(5)-x^4-10*x^3-70*x^2-266*x-80)*exp(x)+(3*x+1)*log(5)^2+(-4*x^2-50*x-16)*log(5)+2*x^3+33*x^2+
208*x+64)/((x*log(5)^2+(-2*x^2-10*x)*log(5)+x^3+10*x^2+25*x)*exp(x)^2+(-2*x*log(5)^2+(4*x^2+26*x)*log(5)-2*x^3
-26*x^2-80*x)*exp(x)+x*log(5)^2+(-2*x^2-16*x)*log(5)+x^3+16*x^2+64*x),x, algorithm="maxima")

[Out]

-(2*x^2 - 3*x*(log(5) - 8) - 3*(x^2 - x*(log(5) - 5))*e^x)/((x - log(5) + 5)*e^x - x + log(5) - 8) + log(x)

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mupad [B]  time = 1.62, size = 91, normalized size = 2.84 \begin {gather*} \frac {24\,x+8\,\ln \relax (x)-3\,x^2\,{\mathrm {e}}^x-5\,{\mathrm {e}}^x\,\ln \relax (x)-3\,x\,\ln \relax (5)-\ln \relax (5)\,\ln \relax (x)-15\,x\,{\mathrm {e}}^x+x\,\ln \relax (x)+2\,x^2+3\,x\,{\mathrm {e}}^x\,\ln \relax (5)+{\mathrm {e}}^x\,\ln \relax (5)\,\ln \relax (x)-x\,{\mathrm {e}}^x\,\ln \relax (x)}{x-\ln \relax (5)-5\,{\mathrm {e}}^x+{\mathrm {e}}^x\,\ln \relax (5)-x\,{\mathrm {e}}^x+8} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((208*x - exp(x)*(266*x - log(5)*(82*x + 10*x^2 + x^3 + 26) + log(5)^2*(6*x + 2) + 70*x^2 + 10*x^3 + x^4 +
80) - log(5)*(50*x + 4*x^2 + 16) + log(5)^2*(3*x + 1) + 33*x^2 + 2*x^3 + exp(2*x)*(85*x - log(5)*(32*x + 6*x^2
+ 10) + log(5)^2*(3*x + 1) + 31*x^2 + 3*x^3 + 25) + 64)/(64*x - log(5)*(16*x + 2*x^2) + x*log(5)^2 + exp(2*x)
*(25*x - log(5)*(10*x + 2*x^2) + x*log(5)^2 + 10*x^2 + x^3) - exp(x)*(80*x - log(5)*(26*x + 4*x^2) + 2*x*log(5
)^2 + 26*x^2 + 2*x^3) + 16*x^2 + x^3),x)

[Out]

(24*x + 8*log(x) - 3*x^2*exp(x) - 5*exp(x)*log(x) - 3*x*log(5) - log(5)*log(x) - 15*x*exp(x) + x*log(x) + 2*x^
2 + 3*x*exp(x)*log(5) + exp(x)*log(5)*log(x) - x*exp(x)*log(x))/(x - log(5) - 5*exp(x) + exp(x)*log(5) - x*exp
(x) + 8)

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sympy [A]  time = 0.44, size = 26, normalized size = 0.81 \begin {gather*} \frac {x^{2}}{- x + \left (x - \log {\relax (5 )} + 5\right ) e^{x} - 8 + \log {\relax (5 )}} + 3 x + \log {\relax (x )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((3*x+1)*ln(5)**2+(-6*x**2-32*x-10)*ln(5)+3*x**3+31*x**2+85*x+25)*exp(x)**2+((-6*x-2)*ln(5)**2+(x**
3+10*x**2+82*x+26)*ln(5)-x**4-10*x**3-70*x**2-266*x-80)*exp(x)+(3*x+1)*ln(5)**2+(-4*x**2-50*x-16)*ln(5)+2*x**3
+33*x**2+208*x+64)/((x*ln(5)**2+(-2*x**2-10*x)*ln(5)+x**3+10*x**2+25*x)*exp(x)**2+(-2*x*ln(5)**2+(4*x**2+26*x)
*ln(5)-2*x**3-26*x**2-80*x)*exp(x)+x*ln(5)**2+(-2*x**2-16*x)*ln(5)+x**3+16*x**2+64*x),x)

[Out]

x**2/(-x + (x - log(5) + 5)*exp(x) - 8 + log(5)) + 3*x + log(x)

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