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

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

[Out]

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

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Rubi [A]  time = 0.03, 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 = {} \[ \int \frac {1}{\left (f+g x^3\right ) \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 8.15, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (f+g x^3\right ) \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.66, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{{\left (g x^{3} + f\right )} \log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 4.98, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (g \,x^{3}+f \right ) \ln \left (c \left (e \,x^{2}+d \right )^{p}\right )^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {e x^{2} + d}{2 \, {\left (e g p x^{4} \log \relax (c) + e f p x \log \relax (c) + {\left (e g p^{2} x^{4} + e f p^{2} x\right )} \log \left (e x^{2} + d\right )\right )}} - \int \frac {2 \, e g x^{5} + 4 \, d g x^{3} - e f x^{2} + d f}{2 \, {\left (e g^{2} p x^{8} \log \relax (c) + 2 \, e f g p x^{5} \log \relax (c) + e f^{2} p x^{2} \log \relax (c) + {\left (e g^{2} p^{2} x^{8} + 2 \, e f g p^{2} x^{5} + e f^{2} p^{2} x^{2}\right )} \log \left (e x^{2} + d\right )\right )}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

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)),x)

[Out]

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

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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