3.114 \(\int x \text {Li}_n(a x) \, dx\)

Optimal. Leaf size=10 \[ \text {Int}(x \text {Li}_n(a x),x) \]

[Out]

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

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Rubi [A]  time = 0.01, 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 = {} \[ \int x \text {PolyLog}(n,a x) \, dx \]

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*}

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Mathematica [A]  time = 0.02, size = 0, normalized size = 0.00 \[ \int x \text {Li}_n(a x) \, dx \]

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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fricas [A]  time = 0.78, size = 0, normalized size = 0.00 \[ {\rm integral}\left (x {\rm polylog}\left (n, a x\right ), x\right ) \]

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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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int x {\rm Li}_{n}(a x)\,{d x} \]

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)

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maple [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int x \polylog \left (n , a x \right )\, dx \]

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 = 0.00, size = 0, normalized size = 0.00 \[ \int x {\rm Li}_{n}(a x)\,{d x} \]

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.10 \[ \int x\,\mathrm {polylog}\left (n,a\,x\right ) \,d x \]

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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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int x \operatorname {Li}_{n}\left (a x\right )\, dx \]

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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