3.160 \(\int \frac{\text{PolyLog}(n,d (F^{c (a+b x)})^p)}{x} \, dx\)

Optimal. Leaf size=22 \[ \text{CannotIntegrate}\left (\frac{\text{PolyLog}\left (n,d \left (F^{a c+b c x}\right )^p\right )}{x},x\right ) \]

[Out]

CannotIntegrate[PolyLog[n, d*(F^(a*c + b*c*x))^p]/x, x]

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Rubi [A]  time = 0.0684746, 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 = {} \[ \int \frac{\text{PolyLog}\left (n,d \left (F^{c (a+b x)}\right )^p\right )}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[PolyLog[n, d*(F^(c*(a + b*x)))^p]/x,x]

[Out]

Defer[Int][PolyLog[n, d*(F^(a*c + b*c*x))^p]/x, x]

Rubi steps

\begin{align*} \int \frac{\text{Li}_n\left (d \left (F^{c (a+b x)}\right )^p\right )}{x} \, dx &=\int \frac{\text{Li}_n\left (d \left (F^{a c+b c x}\right )^p\right )}{x} \, dx\\ \end{align*}

Mathematica [A]  time = 0.0510035, size = 0, normalized size = 0. \[ \int \frac{\text{PolyLog}\left (n,d \left (F^{c (a+b x)}\right )^p\right )}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[PolyLog[n, d*(F^(c*(a + b*x)))^p]/x,x]

[Out]

Integrate[PolyLog[n, d*(F^(c*(a + b*x)))^p]/x, x]

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Maple [A]  time = 0.088, size = 0, normalized size = 0. \begin{align*} \int{\frac{{\it polylog} \left ( n,d \left ({F}^{c \left ( bx+a \right ) } \right ) ^{p} \right ) }{x}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(polylog(n,d*(F^(c*(b*x+a)))^p)/x,x)

[Out]

int(polylog(n,d*(F^(c*(b*x+a)))^p)/x,x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(polylog(n,d*(F^(c*(b*x+a)))^p)/x,x, algorithm="maxima")

[Out]

integrate(polylog(n, (F^((b*x + a)*c))^p*d)/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(polylog(n,d*(F^(c*(b*x+a)))^p)/x,x, algorithm="fricas")

[Out]

integral(polylog(n, (F^(b*c*x + a*c))^p*d)/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(polylog(n,d*(F**(c*(b*x+a)))**p)/x,x)

[Out]

Integral(polylog(n, d*(F**(a*c)*F**(b*c*x))**p)/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(polylog(n,d*(F^(c*(b*x+a)))^p)/x,x, algorithm="giac")

[Out]

integrate(polylog(n, (F^((b*x + a)*c))^p*d)/x, x)