3.4.9 \(\int \frac {1}{(f+g x^3)^2 \log ^2(c (d+e x^2)^p)} \, dx\) [309]

Optimal. Leaf size=27 \[ \text {Int}\left (\frac {1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )},x\right ) \]

[Out]

Unintegrable(1/(g*x^3+f)^2/ln(c*(e*x^2+d)^p)^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 {1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[1/((f + g*x^3)^2*Log[c*(d + e*x^2)^p]^2),x]

[Out]

Defer[Int][1/((f + g*x^3)^2*Log[c*(d + e*x^2)^p]^2), x]

Rubi steps

\begin {align*} \int \frac {1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx &=\int \frac {1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx\\ \end {align*}

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Mathematica [A]
time = 7.58, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\left (f+g x^3\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[1/((f + g*x^3)^2*Log[c*(d + e*x^2)^p]^2),x]

[Out]

Integrate[1/((f + g*x^3)^2*Log[c*(d + e*x^2)^p]^2), x]

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Maple [A]
time = 0.01, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (g \,x^{3}+f \right )^{2} \ln \left (c \left (e \,x^{2}+d \right )^{p}\right )^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(g*x^3+f)^2/ln(c*(e*x^2+d)^p)^2,x)

[Out]

int(1/(g*x^3+f)^2/ln(c*(e*x^2+d)^p)^2,x)

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(g*x^3+f)^2/log(c*(e*x^2+d)^p)^2,x, algorithm="maxima")

[Out]

-1/2*(x^2*e + d)/(g^2*p*x^7*e*log(c) + 2*f*g*p*x^4*e*log(c) + f^2*p*x*e*log(c) + (g^2*p^2*x^7*e + 2*f*g*p^2*x^
4*e + f^2*p^2*x*e)*log(x^2*e + d)) - integrate(1/2*(5*g*x^5*e + 7*d*g*x^3 - f*x^2*e + d*f)/(g^3*p*x^11*e*log(c
) + 3*f*g^2*p*x^8*e*log(c) + 3*f^2*g*p*x^5*e*log(c) + f^3*p*x^2*e*log(c) + (g^3*p^2*x^11*e + 3*f*g^2*p^2*x^8*e
+ 3*f^2*g*p^2*x^5*e + f^3*p^2*x^2*e)*log(x^2*e + d)), x)

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

[Out]

integral(1/((g^2*x^6 + 2*f*g*x^3 + f^2)*log((x^2*e + d)^p*c)^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(1/(g*x**3+f)**2/ln(c*(e*x**2+d)**p)**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(1/(g*x^3+f)^2/log(c*(e*x^2+d)^p)^2,x, algorithm="giac")

[Out]

integrate(1/((g*x^3 + f)^2*log((x^2*e + d)^p*c)^2), x)

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

[Out]

int(1/(log(c*(d + e*x^2)^p)^2*(f + g*x^3)^2), x)

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