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

Optimal. Leaf size=23 \[ \text {Int}\left (\frac {\text {Li}_n\left (d \left (F^{a c+b x c}\right )^p\right )}{x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.07, 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 = {} \[ \int \frac {\text {PolyLog}\left (n,d \left (F^{c (a+b x)}\right )^p\right )}{x} \, dx \]

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*}

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Mathematica [A]  time = 0.05, size = 0, normalized size = 0.00 \[ \int \frac {\text {Li}_n\left (d \left (F^{c (a+b x)}\right )^p\right )}{x} \, dx \]

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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fricas [A]  time = 0.93, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\rm polylog}\left (n, {\left (F^{b c x + a c}\right )}^{p} d\right )}{x}, x\right ) \]

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

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)

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

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

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {\mathrm {polylog}\left (n,d\,{\left (F^{c\,\left (a+b\,x\right )}\right )}^p\right )}{x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

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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