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

Optimal. Leaf size=26 \[ \text {Int}\left (\log \left (f x^m\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^p,x\right ) \]

[Out]

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

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Rubi [A]  time = 0.01, 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 = {} \[ \int \log \left (f x^m\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^p \, dx \]

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*}

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Mathematica [A]  time = 0.10, size = 0, normalized size = 0.00 \[ \int \log \left (f x^m\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^p \, dx \]

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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fricas [A]  time = 0.46, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{p} \log \left (f x^{m}\right ), x\right ) \]

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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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{p} \log \left (f x^{m}\right )\,{d x} \]

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)

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maple [A]  time = 1.40, size = 0, normalized size = 0.00 \[ \int \left (b \ln \left (c \left (e x +d \right )^{n}\right )+a \right )^{p} \ln \left (f \,x^{m}\right )\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: RuntimeError} \]

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 >> ECL says: In function CAR, the value of the first argument is  0which is not
of the expected type LIST

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mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \ln \left (f\,x^m\right )\,{\left (a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )\right )}^p \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

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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