3.377 \(\int \log (f x^m) (a+b \log (c (d+e x)^n))^p \, dx\)

Optimal. Leaf size=25 \[ \text{Unintegrable}\left (\log \left (f x^m\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^p,x\right ) \]

[Out]

Unintegrable[Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^p, x]

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Rubi [A]  time = 0.0101469, 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 = {} \[ \int \log \left (f x^m\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^p \, dx \]

Verification is Not applicable to the result.

[In]

Int[Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^p,x]

[Out]

Defer[Int][Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^p, x]

Rubi steps

\begin{align*} \int \log \left (f x^m\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^p \, dx &=\int \log \left (f x^m\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^p \, dx\\ \end{align*}

Mathematica [A]  time = 0.0901825, size = 0, normalized size = 0. \[ \int \log \left (f x^m\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^p \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^p,x]

[Out]

Integrate[Log[f*x^m]*(a + b*Log[c*(d + e*x)^n])^p, x]

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Maple [A]  time = 0.952, size = 0, normalized size = 0. \begin{align*} \int \ln \left ( f{x}^{m} \right ) \left ( a+b\ln \left ( c \left ( ex+d \right ) ^{n} \right ) \right ) ^{p}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(ln(f*x^m)*(a+b*ln(c*(e*x+d)^n))^p,x)

[Out]

int(ln(f*x^m)*(a+b*ln(c*(e*x+d)^n))^p,x)

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Maxima [F(-2)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: RuntimeError} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(f*x^m)*(a+b*log(c*(e*x+d)^n))^p,x, algorithm="maxima")

[Out]

Exception raised: RuntimeError

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(f*x^m)*(a+b*log(c*(e*x+d)^n))^p,x, algorithm="fricas")

[Out]

integral((b*log((e*x + d)^n*c) + a)^p*log(f*x^m), x)

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(ln(f*x**m)*(a+b*ln(c*(e*x+d)**n))**p,x)

[Out]

Timed out

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{p} \log \left (f x^{m}\right )\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(f*x^m)*(a+b*log(c*(e*x+d)^n))^p,x, algorithm="giac")

[Out]

integrate((b*log((e*x + d)^n*c) + a)^p*log(f*x^m), x)