3.134 \(\int \frac {\text {Li}_3(c (a+b x))}{x} \, dx\)

Optimal. Leaf size=17 \[ \text {Int}\left (\frac {\text {Li}_3(a c+b x c)}{x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.04, 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 = {} \[ \int \frac {\text {PolyLog}(3,c (a+b x))}{x} \, dx \]

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*}

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Mathematica [A]  time = 0.04, size = 0, normalized size = 0.00 \[ \int \frac {\text {Li}_3(c (a+b x))}{x} \, dx \]

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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fricas [A]  time = 1.22, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\rm polylog}\left (3, b c x + a c\right )}{x}, x\right ) \]

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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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\rm Li}_{3}({\left (b x + a\right )} c)}{x}\,{d x} \]

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)

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maple [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\polylog \left (3, c \left (b x +a \right )\right )}{x}\, dx \]

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 = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\rm Li}_{3}({\left (b x + a\right )} c)}{x}\,{d x} \]

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {\mathrm {polylog}\left (3,c\,\left (a+b\,x\right )\right )}{x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(polylog(3, c*(a + b*x))/x,x)

[Out]

int(polylog(3, c*(a + b*x))/x, x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {Li}_{3}\left (a c + b c x\right )}{x}\, dx \]

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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