3.297 \(\int \frac{\log ^2(c (d+e x^2)^p)}{(f+g x^3)^2} \, dx\)

Optimal. Leaf size=26 \[ \text{Unintegrable}\left (\frac{\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^3\right )^2},x\right ) \]

[Out]

Unintegrable[Log[c*(d + e*x^2)^p]^2/(f + g*x^3)^2, x]

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Rubi [A]  time = 0.0255872, 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 = {} \[ \int \frac{\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^3\right )^2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Log[c*(d + e*x^2)^p]^2/(f + g*x^3)^2,x]

[Out]

Defer[Int][Log[c*(d + e*x^2)^p]^2/(f + g*x^3)^2, x]

Rubi steps

\begin{align*} \int \frac{\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^3\right )^2} \, dx &=\int \frac{\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^3\right )^2} \, dx\\ \end{align*}

Mathematica [A]  time = 22.5065, size = 0, normalized size = 0. \[ \int \frac{\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^3\right )^2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Log[c*(d + e*x^2)^p]^2/(f + g*x^3)^2,x]

[Out]

Integrate[Log[c*(d + e*x^2)^p]^2/(f + g*x^3)^2, x]

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Maple [F]  time = 180., size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( \ln \left ( c \left ( e{x}^{2}+d \right ) ^{p} \right ) \right ) ^{2}}{ \left ( g{x}^{3}+f \right ) ^{2}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(ln(c*(e*x^2+d)^p)^2/(g*x^3+f)^2,x)

[Out]

int(ln(c*(e*x^2+d)^p)^2/(g*x^3+f)^2,x)

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Maxima [F(-2)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(c*(e*x^2+d)^p)^2/(g*x^3+f)^2,x, algorithm="maxima")

[Out]

Exception raised: ValueError

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}}{g^{2} x^{6} + 2 \, f g x^{3} + f^{2}}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(c*(e*x^2+d)^p)^2/(g*x^3+f)^2,x, algorithm="fricas")

[Out]

integral(log((e*x^2 + d)^p*c)^2/(g^2*x^6 + 2*f*g*x^3 + f^2), 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(ln(c*(e*x**2+d)**p)**2/(g*x**3+f)**2,x)

[Out]

Timed out

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}}{{\left (g x^{3} + f\right )}^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(c*(e*x^2+d)^p)^2/(g*x^3+f)^2,x, algorithm="giac")

[Out]

integrate(log((e*x^2 + d)^p*c)^2/(g*x^3 + f)^2, x)