3.161 \(\int \frac{(f x)^m}{\log (c (d+e x^2)^p)} \, dx\)

Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{(f x)^m}{\log \left (c \left (d+e x^2\right )^p\right )},x\right ) \]

[Out]

Unintegrable[(f*x)^m/Log[c*(d + e*x^2)^p], x]

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Rubi [A]  time = 0.0181375, 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 = {} \[ \int \frac{(f x)^m}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(f*x)^m/Log[c*(d + e*x^2)^p],x]

[Out]

Defer[Int][(f*x)^m/Log[c*(d + e*x^2)^p], x]

Rubi steps

\begin{align*} \int \frac{(f x)^m}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx &=\int \frac{(f x)^m}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx\\ \end{align*}

Mathematica [A]  time = 0.3338, size = 0, normalized size = 0. \[ \int \frac{(f x)^m}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(f*x)^m/Log[c*(d + e*x^2)^p],x]

[Out]

Integrate[(f*x)^m/Log[c*(d + e*x^2)^p], x]

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Maple [A]  time = 0.957, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( fx \right ) ^{m}}{\ln \left ( c \left ( e{x}^{2}+d \right ) ^{p} \right ) }}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((f*x)^m/ln(c*(e*x^2+d)^p),x)

[Out]

int((f*x)^m/ln(c*(e*x^2+d)^p),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (f x\right )^{m}}{\log \left ({\left (e x^{2} + d\right )}^{p} c\right )}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((f*x)^m/log(c*(e*x^2+d)^p),x, algorithm="maxima")

[Out]

integrate((f*x)^m/log((e*x^2 + d)^p*c), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\left (f x\right )^{m}}{\log \left ({\left (e x^{2} + d\right )}^{p} c\right )}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((f*x)^m/log(c*(e*x^2+d)^p),x, algorithm="fricas")

[Out]

integral((f*x)^m/log((e*x^2 + d)^p*c), 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((f*x)**m/ln(c*(e*x**2+d)**p),x)

[Out]

Timed out

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (f x\right )^{m}}{\log \left ({\left (e x^{2} + d\right )}^{p} c\right )}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((f*x)^m/log(c*(e*x^2+d)^p),x, algorithm="giac")

[Out]

integrate((f*x)^m/log((e*x^2 + d)^p*c), x)