3.180 \(\int \frac{(g+h \log (f (d+e x)^n)) \text{PolyLog}(2,c (a+b x))}{x} \, dx\)

Optimal. Leaf size=29 \[ \text{Unintegrable}\left (\frac{\text{PolyLog}(2,c (a+b x)) \left (h \log \left (f (d+e x)^n\right )+g\right )}{x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0250694, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., 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*}

Mathematica [A]  time = 0.552935, size = 0, normalized size = 0. \[ \int \frac{\left (g+h \log \left (f (d+e x)^n\right )\right ) \text{PolyLog}(2,c (a+b x))}{x} \, dx \]

Verification is Not applicable to the result.

[In]

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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Maple [A]  time = 0.302, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( g+h\ln \left ( f \left ( ex+d \right ) ^{n} \right ) \right ){\it polylog} \left ( 2,c \left ( bx+a \right ) \right ) }{x}}\, dx \end{align*}

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., size = 0, normalized size = 0. \begin{align*} \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} \end{align*}

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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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\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 ) \end{align*}

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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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

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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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \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} \end{align*}

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)