3.3.97 \(\int \frac {\log ^2(c (d+e x^2)^p)}{(f+g x^3)^2} \, dx\) [297]

Optimal. Leaf size=27 \[ \text {Int}\left (\frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^3\right )^2},x\right ) \]

[Out]

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

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Rubi [A]
time = 0.02, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^3\right )^2} \, dx \end {gather*}

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*}

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Mathematica [A]
time = 29.67, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\log ^2\left (c \left (d+e x^2\right )^p\right )}{\left (f+g x^3\right )^2} \, dx \end {gather*}

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 [A]
time = 0.38, size = 0, normalized size = 0.00 \[\int \frac {\ln \left (c \left (e \,x^{2}+d \right )^{p}\right )^{2}}{\left (g \,x^{3}+f \right )^{2}}\, dx\]

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(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

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]

Timed out

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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

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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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((x^2*e + d)^p*c)^2/(g*x^3 + f)^2, x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\ln \left (c\,{\left (e\,x^2+d\right )}^p\right )}^2}{{\left (g\,x^3+f\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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