3.134 \(\int \frac{\text{PolyLog}(3,c (a+b x))}{x} \, dx\)

Optimal. Leaf size=16 \[ \text{Int}\left (\frac{\text{PolyLog}(3,a c+b c x)}{x},x\right ) \]

[Out]

Int[PolyLog[3, a*c + b*c*x]/x, x]

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Rubi [A]  time = 0.0377706, 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 = {} \[ \int \frac{\text{PolyLog}(3,c (a+b x))}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[PolyLog[3, c*(a + b*x)]/x,x]

[Out]

Defer[Int][PolyLog[3, a*c + b*c*x]/x, x]

Rubi steps

\begin{align*} \int \frac{\text{Li}_3(c (a+b x))}{x} \, dx &=\int \frac{\text{Li}_3(a c+b c x)}{x} \, dx\\ \end{align*}

Mathematica [A]  time = 0.0369997, size = 0, normalized size = 0. \[ \int \frac{\text{PolyLog}(3,c (a+b x))}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[PolyLog[3, c*(a + b*x)]/x,x]

[Out]

Integrate[PolyLog[3, c*(a + b*x)]/x, x]

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Maple [A]  time = 0.004, size = 0, normalized size = 0. \begin{align*} \int{\frac{{\it polylog} \left ( 3,c \left ( bx+a \right ) \right ) }{x}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(polylog(3,c*(b*x+a))/x,x)

[Out]

int(polylog(3,c*(b*x+a))/x,x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(polylog(3,c*(b*x+a))/x,x, algorithm="maxima")

[Out]

integrate(polylog(3, (b*x + a)*c)/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(polylog(3,c*(b*x+a))/x,x, algorithm="fricas")

[Out]

integral(polylog(3, b*c*x + a*c)/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(polylog(3,c*(b*x+a))/x,x)

[Out]

Integral(polylog(3, a*c + b*c*x)/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(polylog(3,c*(b*x+a))/x,x, algorithm="giac")

[Out]

integrate(polylog(3, (b*x + a)*c)/x, x)