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

Optimal. Leaf size=26 \[ \text {Int}\left (\frac {\text {Li}_k\left (e x^q\right ) \left (a+b \log \left (c x^n\right )\right )^p}{x},x\right ) \]

[Out]

Unintegrable((a+b*ln(c*x^n))^p*polylog(k,e*x^q)/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 = {} \[ \int \frac {\left (a+b \log \left (c x^n\right )\right )^p \text {PolyLog}\left (k,e x^q\right )}{x} \, dx \]

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*}

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Mathematica [A]  time = 0.05, size = 0, normalized size = 0.00 \[ \int \frac {\left (a+b \log \left (c x^n\right )\right )^p \text {Li}_k\left (e x^q\right )}{x} \, dx \]

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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fricas [A]  time = 0.89, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (b \log \left (c x^{n}\right ) + a\right )}^{p} {\rm polylog}\left (k, e x^{q}\right )}{x}, x\right ) \]

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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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (b \log \left (c x^{n}\right ) + a\right )}^{p} {\rm Li}_{k}(e x^{q})}{x}\,{d x} \]

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)

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maple [A]  time = 0.07, size = 0, normalized size = 0.00 \[ \int \frac {\left (b \ln \left (c \,x^{n}\right )+a \right )^{p} \polylog \left (k , e \,x^{q}\right )}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (b \log \left (c x^{n}\right ) + a\right )}^{p} {\rm Li}_{k}(e x^{q})}{x}\,{d x} \]

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {\mathrm {polylog}\left (k,e\,x^q\right )\,{\left (a+b\,\ln \left (c\,x^n\right )\right )}^p}{x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (a + b \log {\left (c x^{n} \right )}\right )^{p} \operatorname {Li}_{k}\left (e x^{q}\right )}{x}\, dx \]

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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