3.114 \(\int x \text{PolyLog}(n,a x) \, dx\)

Optimal. Leaf size=9 \[ \text{Unintegrable}(x \text{PolyLog}(n,a x),x) \]

[Out]

Unintegrable[x*PolyLog[n, a*x], x]

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Rubi [A]  time = 0.0054963, 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 = {} \[ \int x \text{PolyLog}(n,a x) \, dx \]

Verification is Not applicable to the result.

[In]

Int[x*PolyLog[n, a*x],x]

[Out]

Defer[Int][x*PolyLog[n, a*x], x]

Rubi steps

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

Mathematica [A]  time = 0.0216945, size = 0, normalized size = 0. \[ \int x \text{PolyLog}(n,a x) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[x*PolyLog[n, a*x],x]

[Out]

Integrate[x*PolyLog[n, a*x], x]

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Maple [A]  time = 0.05, size = 0, normalized size = 0. \begin{align*} \int x{\it polylog} \left ( n,ax \right ) \, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x*polylog(n,a*x),x)

[Out]

int(x*polylog(n,a*x),x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x*polylog(n, a*x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(x*polylog(n, a*x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(x*polylog(n, a*x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x*polylog(n, a*x), x)