3.2.80 \(\int \frac {(g+h \log (f (d+e x)^n)) \text {PolyLog}(2,c (a+b x))}{x} \, dx\) [180]

Optimal. Leaf size=30 \[ \text {Int}\left (\frac {\left (g+h \log \left (f (d+e x)^n\right )\right ) \text {PolyLog}(2,c (a+b x))}{x},x\right ) \]

[Out]

Unintegrable((g+h*ln(f*(e*x+d)^n))*polylog(2,c*(b*x+a))/x,x)

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Rubi [A]
time = 0.02, 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 \frac {\left (g+h \log \left (f (d+e x)^n\right )\right ) \text {Li}_2(c (a+b x))}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((g + h*Log[f*(d + e*x)^n])*PolyLog[2, c*(a + b*x)])/x,x]

[Out]

Defer[Int][((g + h*Log[f*(d + e*x)^n])*PolyLog[2, c*(a + b*x)])/x, x]

Rubi steps

\begin {align*} \int \frac {\left (g+h \log \left (f (d+e x)^n\right )\right ) \text {Li}_2(c (a+b x))}{x} \, dx &=\int \frac {\left (g+h \log \left (f (d+e x)^n\right )\right ) \text {Li}_2(c (a+b x))}{x} \, dx\\ \end {align*}

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Mathematica [A]
time = 1.77, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (g+h \log \left (f (d+e x)^n\right )\right ) \text {PolyLog}(2,c (a+b x))}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[((g + h*Log[f*(d + e*x)^n])*PolyLog[2, c*(a + b*x)])/x,x]

[Out]

Integrate[((g + h*Log[f*(d + e*x)^n])*PolyLog[2, c*(a + b*x)])/x, x]

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Maple [A]
time = 0.10, size = 0, normalized size = 0.00 \[\int \frac {\left (g +h \ln \left (f \left (e x +d \right )^{n}\right )\right ) \polylog \left (2, c \left (b x +a \right )\right )}{x}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((g+h*ln(f*(e*x+d)^n))*polylog(2,c*(b*x+a))/x,x)

[Out]

int((g+h*ln(f*(e*x+d)^n))*polylog(2,c*(b*x+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((g+h*log(f*(e*x+d)^n))*polylog(2,c*(b*x+a))/x,x, algorithm="maxima")

[Out]

integrate((h*log((x*e + d)^n*f) + g)*dilog((b*x + a)*c)/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((g+h*log(f*(e*x+d)^n))*polylog(2,c*(b*x+a))/x,x, algorithm="fricas")

[Out]

integral((h*dilog(b*c*x + a*c)*log((x*e + d)^n*f) + g*dilog(b*c*x + a*c))/x, x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (g + h \log {\left (f \left (d + e x\right )^{n} \right )}\right ) \operatorname {Li}_{2}\left (a c + b c x\right )}{x}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((g+h*ln(f*(e*x+d)**n))*polylog(2,c*(b*x+a))/x,x)

[Out]

Integral((g + h*log(f*(d + e*x)**n))*polylog(2, a*c + b*c*x)/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((g+h*log(f*(e*x+d)^n))*polylog(2,c*(b*x+a))/x,x, algorithm="giac")

[Out]

integrate((h*log((e*x + d)^n*f) + g)*dilog((b*x + a)*c)/x, x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {\mathrm {polylog}\left (2,c\,\left (a+b\,x\right )\right )\,\left (g+h\,\ln \left (f\,{\left (d+e\,x\right )}^n\right )\right )}{x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((polylog(2, c*(a + b*x))*(g + h*log(f*(d + e*x)^n)))/x,x)

[Out]

int((polylog(2, c*(a + b*x))*(g + h*log(f*(d + e*x)^n)))/x, x)

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