Optimal. Leaf size=30 \[ \text {Int}\left (\frac {\text {Li}_2(c (a+b x)) \left (h \log \left (f (d+e x)^n\right )+g\right )}{x},x\right ) \]
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Rubi [A] time = 0.03, 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 = {} \[ \int \frac {\left (g+h \log \left (f (d+e x)^n\right )\right ) \text {PolyLog}(2,c (a+b x))}{x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\left (g+h \log \left (f (d+e x)^n\right )\right ) \text {Li}_2(c (a+b x))}{x} \, dx &=\int \frac {\left (g+h \log \left (f (d+e x)^n\right )\right ) \text {Li}_2(c (a+b x))}{x} \, dx\\ \end {align*}
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Mathematica [A] time = 2.43, size = 0, normalized size = 0.00 \[ \int \frac {\left (g+h \log \left (f (d+e x)^n\right )\right ) \text {Li}_2(c (a+b x))}{x} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 1.37, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {h {\rm Li}_2\left (b c x + a c\right ) \log \left ({\left (e x + d\right )}^{n} f\right ) + g {\rm Li}_2\left (b c x + a c\right )}{x}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (h \log \left ({\left (e x + d\right )}^{n} f\right ) + g\right )} {\rm Li}_2\left ({\left (b x + a\right )} c\right )}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.26, size = 0, normalized size = 0.00 \[ \int \frac {\left (g +h \ln \left (f \left (e x +d \right )^{n}\right )\right ) \polylog \left (2, c \left (b x +a \right )\right )}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (h \log \left ({\left (e x + d\right )}^{n} f\right ) + g\right )} {\rm Li}_2\left ({\left (b x + a\right )} c\right )}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {\mathrm {polylog}\left (2,c\,\left (a+b\,x\right )\right )\,\left (g+h\,\ln \left (f\,{\left (d+e\,x\right )}^n\right )\right )}{x} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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