3.1.100 \(\int \text {PolyLog}(-\frac {5}{2},a x) \, dx\) [100]

Optimal. Leaf size=30 \[ x \text {PolyLog}\left (-\frac {3}{2},a x\right )-x \text {PolyLog}\left (-\frac {1}{2},a x\right )+\text {Int}\left (\text {PolyLog}\left (-\frac {1}{2},a x\right ),x\right ) \]

[Out]

x*polylog(-3/2,a*x)-x*polylog(-1/2,a*x)+Unintegrable(polylog(-1/2,a*x),x)

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Rubi [A]
time = 0.00, 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 = {} \begin {gather*} \int \text {Li}_{-\frac {5}{2}}(a x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[PolyLog[-5/2, a*x],x]

[Out]

x*PolyLog[-3/2, a*x] - x*PolyLog[-1/2, a*x] + Defer[Int][PolyLog[-1/2, a*x], x]

Rubi steps

\begin {align*} \int \text {Li}_{-\frac {5}{2}}(a x) \, dx &=x \text {Li}_{-\frac {3}{2}}(a x)-\int \text {Li}_{-\frac {3}{2}}(a x) \, dx\\ &=x \text {Li}_{-\frac {3}{2}}(a x)-x \text {Li}_{-\frac {1}{2}}(a x)+\int \text {Li}_{-\frac {1}{2}}(a x) \, dx\\ \end {align*}

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Mathematica [A]
time = 0.01, size = 0, normalized size = 0.00 \begin {gather*} \int \text {PolyLog}\left (-\frac {5}{2},a x\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[PolyLog[-5/2, a*x],x]

[Out]

Integrate[PolyLog[-5/2, a*x], x]

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Maple [A]
time = 0.02, size = 0, normalized size = 0.00 \[\int \polylog \left (-\frac {5}{2}, a x \right )\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(polylog(-5/2,a*x),x)

[Out]

int(polylog(-5/2,a*x),x)

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(polylog(-5/2,a*x),x, algorithm="maxima")

[Out]

integrate(polylog(-5/2, a*x), x)

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(polylog(-5/2,a*x),x, algorithm="fricas")

[Out]

integral(polylog(-5/2, a*x), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \operatorname {Li}_{- \frac {5}{2}}\left (a x\right )\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(polylog(-5/2,a*x),x)

[Out]

Integral(polylog(-5/2, a*x), x)

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(polylog(-5/2,a*x),x, algorithm="giac")

[Out]

integrate(polylog(-5/2, a*x), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \mathrm {polylog}\left (-\frac {5}{2},a\,x\right ) \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(polylog(-5/2, a*x),x)

[Out]

int(polylog(-5/2, a*x), x)

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