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

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

[Out]

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

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Rubi [A]  time = 0.0244526, 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 = {} \[ \int \frac{\left (f+g x^2\right )^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 0.471791, size = 0, normalized size = 0. \[ \int \frac{\left (f+g x^2\right )^2}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.782, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( g{x}^{2}+f \right ) ^{2}}{\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)^2/ln(c*(e*x^2+d)^p),x)

[Out]

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

[Out]

integrate((g*x^2 + f)^2/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^{2} x^{4} + 2 \, f g x^{2} + f^{2}}{\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)^2/log(c*(e*x^2+d)^p),x, algorithm="fricas")

[Out]

integral((g^2*x^4 + 2*f*g*x^2 + f^2)/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{\left (f + g x^{2}\right )^{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)**2/ln(c*(e*x**2+d)**p),x)

[Out]

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

[Out]

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