3.198 \(\int \frac{(a+b \log (c x^n))^p \text{PolyLog}(k,e x^q)}{x} \, dx\)

Optimal. Leaf size=25 \[ \text{Unintegrable}\left (\frac{\text{PolyLog}\left (k,e x^q\right ) \left (a+b \log \left (c x^n\right )\right )^p}{x},x\right ) \]

[Out]

Unintegrable[((a + b*Log[c*x^n])^p*PolyLog[k, e*x^q])/x, x]

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Rubi [A]  time = 0.0331453, 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 = {} \[ \int \frac{\left (a+b \log \left (c x^n\right )\right )^p \text{PolyLog}\left (k,e x^q\right )}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[((a + b*Log[c*x^n])^p*PolyLog[k, e*x^q])/x,x]

[Out]

Defer[Int][((a + b*Log[c*x^n])^p*PolyLog[k, e*x^q])/x, x]

Rubi steps

\begin{align*} \int \frac{\left (a+b \log \left (c x^n\right )\right )^p \text{Li}_k\left (e x^q\right )}{x} \, dx &=\int \frac{\left (a+b \log \left (c x^n\right )\right )^p \text{Li}_k\left (e x^q\right )}{x} \, dx\\ \end{align*}

Mathematica [A]  time = 0.0484784, size = 0, normalized size = 0. \[ \int \frac{\left (a+b \log \left (c x^n\right )\right )^p \text{PolyLog}\left (k,e x^q\right )}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[((a + b*Log[c*x^n])^p*PolyLog[k, e*x^q])/x,x]

[Out]

Integrate[((a + b*Log[c*x^n])^p*PolyLog[k, e*x^q])/x, x]

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Maple [A]  time = 0.033, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( a+b\ln \left ( c{x}^{n} \right ) \right ) ^{p}{\it polylog} \left ( k,e{x}^{q} \right ) }{x}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a+b*ln(c*x^n))^p*polylog(k,e*x^q)/x,x)

[Out]

int((a+b*ln(c*x^n))^p*polylog(k,e*x^q)/x,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (b \log \left (c x^{n}\right ) + a\right )}^{p}{\rm Li}_{k}(e x^{q})}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*log(c*x^n))^p*polylog(k,e*x^q)/x,x, algorithm="maxima")

[Out]

integrate((b*log(c*x^n) + a)^p*polylog(k, e*x^q)/x, x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{{\left (b \log \left (c x^{n}\right ) + a\right )}^{p}{\rm polylog}\left (k, e x^{q}\right )}{x}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*log(c*x^n))^p*polylog(k,e*x^q)/x,x, algorithm="fricas")

[Out]

integral((b*log(c*x^n) + a)^p*polylog(k, e*x^q)/x, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (a + b \log{\left (c x^{n} \right )}\right )^{p} \operatorname{Li}_{k}\left (e x^{q}\right )}{x}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*ln(c*x**n))**p*polylog(k,e*x**q)/x,x)

[Out]

Integral((a + b*log(c*x**n))**p*polylog(k, e*x**q)/x, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (b \log \left (c x^{n}\right ) + a\right )}^{p}{\rm Li}_{k}(e x^{q})}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*log(c*x^n))^p*polylog(k,e*x^q)/x,x, algorithm="giac")

[Out]

integrate((b*log(c*x^n) + a)^p*polylog(k, e*x^q)/x, x)