3.180 \(\int \frac {(g+h \log (f (d+e x)^n)) \text {Li}_2(c (a+b x))}{x} \, dx\)

Optimal. Leaf size=30 \[ \text {Int}\left (\frac {\text {Li}_2(c (a+b x)) \left (h \log \left (f (d+e x)^n\right )+g\right )}{x},x\right ) \]

[Out]

Unintegrable((g+h*ln(f*(e*x+d)^n))*polylog(2,c*(b*x+a))/x,x)

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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.

[In]

Int[((g + h*Log[f*(d + e*x)^n])*PolyLog[2, c*(a + b*x)])/x,x]

[Out]

Defer[Int][((g + h*Log[f*(d + e*x)^n])*PolyLog[2, c*(a + b*x)])/x, x]

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.

[In]

Integrate[((g + h*Log[f*(d + e*x)^n])*PolyLog[2, c*(a + b*x)])/x,x]

[Out]

Integrate[((g + h*Log[f*(d + e*x)^n])*PolyLog[2, c*(a + b*x)])/x, x]

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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.

[In]

integrate((g+h*log(f*(e*x+d)^n))*polylog(2,c*(b*x+a))/x,x, algorithm="fricas")

[Out]

integral((h*dilog(b*c*x + a*c)*log((e*x + d)^n*f) + g*dilog(b*c*x + a*c))/x, x)

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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.

[In]

integrate((g+h*log(f*(e*x+d)^n))*polylog(2,c*(b*x+a))/x,x, algorithm="giac")

[Out]

integrate((h*log((e*x + d)^n*f) + g)*dilog((b*x + a)*c)/x, x)

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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.

[In]

int((g+h*ln(f*(e*x+d)^n))*polylog(2,c*(b*x+a))/x,x)

[Out]

int((g+h*ln(f*(e*x+d)^n))*polylog(2,c*(b*x+a))/x,x)

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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.

[In]

integrate((g+h*log(f*(e*x+d)^n))*polylog(2,c*(b*x+a))/x,x, algorithm="maxima")

[Out]

integrate((h*log((e*x + d)^n*f) + g)*dilog((b*x + a)*c)/x, x)

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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.

[In]

int((polylog(2, c*(a + b*x))*(g + h*log(f*(d + e*x)^n)))/x,x)

[Out]

int((polylog(2, c*(a + b*x))*(g + h*log(f*(d + e*x)^n)))/x, x)

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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.

[In]

integrate((g+h*ln(f*(e*x+d)**n))*polylog(2,c*(b*x+a))/x,x)

[Out]

Timed out

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