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

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

[Out]

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

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Rubi [A]  time = 0.0112972, 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 = {} \[ \int \frac{\log \left (f x^m\right )}{a+b \log \left (c (d+e x)^n\right )} \, dx \]

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*}

Mathematica [A]  time = 0.0419448, size = 0, normalized size = 0. \[ \int \frac{\log \left (f x^m\right )}{a+b \log \left (c (d+e x)^n\right )} \, dx \]

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 = 2.376, size = 0, normalized size = 0. \begin{align*} \int{\frac{\ln \left ( f{x}^{m} \right ) }{a+b\ln \left ( c \left ( ex+d \right ) ^{n} \right ) }}\, 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)),x)

[Out]

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

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

[Out]

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

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

[Out]

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

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

[Out]

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

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

[Out]

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