3.4.75 \(\int \frac {\log (f x^m)}{a+b \log (c (d+e x)^n)} \, dx\) [375]

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

[Out]

Unintegrable(ln(f*x^m)/(a+b*ln(c*(e*x+d)^n)),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 = {} \begin {gather*} \int \frac {\log \left (f x^m\right )}{a+b \log \left (c (d+e x)^n\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]
time = 0.03, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\log \left (f x^m\right )}{a+b \log \left (c (d+e x)^n\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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Maple [A]
time = 0.04, size = 0, normalized size = 0.00 \[\int \frac {\ln \left (f \,x^{m}\right )}{a +b \ln \left (c \left (e x +d \right )^{n}\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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