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

Optimal. Leaf size=24 \[ \text{Unintegrable}\left (\frac{f+g x^2}{\log \left (c \left (d+e x^2\right )^p\right )},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0143442, 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 = {} \[ \int \frac{f+g x^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 0.29989, size = 0, normalized size = 0. \[ \int \frac{f+g x^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.512, size = 0, normalized size = 0. \begin{align*} \int{\frac{g{x}^{2}+f}{\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((g*x^2+f)/ln(c*(e*x^2+d)^p),x)

[Out]

int((g*x^2+f)/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{g x^{2} + f}{\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((g*x^2+f)/log(c*(e*x^2+d)^p),x, algorithm="maxima")

[Out]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((g*x**2+f)/ln(c*(e*x**2+d)**p),x)

[Out]

Integral((f + g*x**2)/log(c*(d + e*x**2)**p), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{g x^{2} + f}{\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((g*x^2+f)/log(c*(e*x^2+d)^p),x, algorithm="giac")

[Out]

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