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

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

[Out]

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

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 0.04, size = 0, normalized size = 0.00 \[ \int \frac {\text {Li}_k\left (e x^q\right )}{x \left (a+b \log \left (c x^n\right )\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.78, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\rm polylog}\left (k, e x^{q}\right )}{b x \log \left (c x^{n}\right ) + a x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.06, size = 0, normalized size = 0.00 \[ \int \frac {\polylog \left (k , e \,x^{q}\right )}{\left (b \ln \left (c \,x^{n}\right )+a \right ) x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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