3.118 \(\int \frac{\text{PolyLog}(n,a x)}{x^3} \, dx\)

Optimal. Leaf size=11 \[ \text{Unintegrable}\left (\frac{\text{PolyLog}(n,a x)}{x^3},x\right ) \]

[Out]

Unintegrable[PolyLog[n, a*x]/x^3, x]

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Rubi [A]  time = 0.0089528, 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 = {} \[ \int \frac{\text{PolyLog}(n,a x)}{x^3} \, dx \]

Verification is Not applicable to the result.

[In]

Int[PolyLog[n, a*x]/x^3,x]

[Out]

Defer[Int][PolyLog[n, a*x]/x^3, x]

Rubi steps

\begin{align*} \int \frac{\text{Li}_n(a x)}{x^3} \, dx &=\int \frac{\text{Li}_n(a x)}{x^3} \, dx\\ \end{align*}

Mathematica [A]  time = 0.0208255, size = 0, normalized size = 0. \[ \int \frac{\text{PolyLog}(n,a x)}{x^3} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[PolyLog[n, a*x]/x^3,x]

[Out]

Integrate[PolyLog[n, a*x]/x^3, x]

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Maple [A]  time = 0.049, size = 0, normalized size = 0. \begin{align*} \int{\frac{{\it polylog} \left ( n,ax \right ) }{{x}^{3}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(polylog(n,a*x)/x^3,x)

[Out]

int(polylog(n,a*x)/x^3,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\rm Li}_{n}(a x)}{x^{3}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(polylog(n,a*x)/x^3,x, algorithm="maxima")

[Out]

integrate(polylog(n, a*x)/x^3, x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{{\rm polylog}\left (n, a x\right )}{x^{3}}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(polylog(n,a*x)/x^3,x, algorithm="fricas")

[Out]

integral(polylog(n, a*x)/x^3, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{Li}_{n}\left (a x\right )}{x^{3}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(polylog(n,a*x)/x**3,x)

[Out]

Integral(polylog(n, a*x)/x**3, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\rm Li}_{n}(a x)}{x^{3}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(polylog(n,a*x)/x^3,x, algorithm="giac")

[Out]

integrate(polylog(n, a*x)/x^3, x)