Optimal. Leaf size=13 \[ \frac {\text {Li}_{n+1}\left (a x^q\right )}{q} \]
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Rubi [A] time = 0.01, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {6589} \[ \frac {\text {PolyLog}\left (n+1,a x^q\right )}{q} \]
Antiderivative was successfully verified.
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Rule 6589
Rubi steps
\begin {align*} \int \frac {\text {Li}_n\left (a x^q\right )}{x} \, dx &=\frac {\text {Li}_{1+n}\left (a x^q\right )}{q}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \[ \frac {\text {Li}_{n+1}\left (a x^q\right )}{q} \]
Antiderivative was successfully verified.
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fricas [F] time = 1.03, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\rm polylog}\left (n, a x^{q}\right )}{x}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\rm Li}_{n}(a x^{q})}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 1.08 \[ \frac {\polylog \left (1+n , a \,x^{q}\right )}{q} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\rm Li}_{n}(a x^{q})}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.08 \[ \int \frac {\mathrm {polylog}\left (n,a\,x^q\right )}{x} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {Li}_{n}\left (a x^{q}\right )}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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