3.282 \(\int \frac{1}{(f+g x^2) \log (c (d+e x^2)^p)} \, dx\)

Optimal. Leaf size=26 \[ \text{Unintegrable}\left (\frac{1}{\left (f+g x^2\right ) \log \left (c \left (d+e x^2\right )^p\right )},x\right ) \]

[Out]

Unintegrable[1/((f + g*x^2)*Log[c*(d + e*x^2)^p]), x]

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Rubi [A]  time = 0.0278251, 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 = {} \[ \int \frac{1}{\left (f+g x^2\right ) \log \left (c \left (d+e x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/((f + g*x^2)*Log[c*(d + e*x^2)^p]),x]

[Out]

Defer[Int][1/((f + g*x^2)*Log[c*(d + e*x^2)^p]), x]

Rubi steps

\begin{align*} \int \frac{1}{\left (f+g x^2\right ) \log \left (c \left (d+e x^2\right )^p\right )} \, dx &=\int \frac{1}{\left (f+g x^2\right ) \log \left (c \left (d+e x^2\right )^p\right )} \, dx\\ \end{align*}

Mathematica [A]  time = 0.547717, size = 0, normalized size = 0. \[ \int \frac{1}{\left (f+g x^2\right ) \log \left (c \left (d+e x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/((f + g*x^2)*Log[c*(d + e*x^2)^p]),x]

[Out]

Integrate[1/((f + g*x^2)*Log[c*(d + e*x^2)^p]), x]

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Maple [A]  time = 1.013, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( g{x}^{2}+f \right ) \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(1/(g*x^2+f)/ln(c*(e*x^2+d)^p),x)

[Out]

int(1/(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{1}{{\left (g x^{2} + f\right )} \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(1/(g*x^2+f)/log(c*(e*x^2+d)^p),x, algorithm="maxima")

[Out]

integrate(1/((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{1}{{\left (g x^{2} + f\right )} \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(1/(g*x^2+f)/log(c*(e*x^2+d)^p),x, algorithm="fricas")

[Out]

integral(1/((g*x^2 + f)*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(1/(g*x**2+f)/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{1}{{\left (g x^{2} + f\right )} \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(1/(g*x^2+f)/log(c*(e*x^2+d)^p),x, algorithm="giac")

[Out]

integrate(1/((g*x^2 + f)*log((e*x^2 + d)^p*c)), x)