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

Optimal. Leaf size=21 \[ \text {Int}\left (\frac {1}{x^2 \log ^2\left (c \left (d+e x^3\right )^p\right )},x\right ) \]

[Out]

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

________________________________________________________________________________________

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

Verification is Not applicable to the result.

[In]

Int[1/(x^2*Log[c*(d + e*x^3)^p]^2),x]

[Out]

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

Rubi steps

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

________________________________________________________________________________________

Mathematica [A]  time = 1.31, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^2 \log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

________________________________________________________________________________________

fricas [A]  time = 0.45, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{x^{2} \log \left ({\left (e x^{3} + d\right )}^{p} c\right )^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

maple [A]  time = 4.24, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{2} \ln \left (c \left (e \,x^{3}+d \right )^{p}\right )^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {1}{x^2\,{\ln \left (c\,{\left (e\,x^3+d\right )}^p\right )}^2} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x^2*log(c*(d + e*x^3)^p)^2),x)

[Out]

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

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(1/(x**2*log(c*(d + e*x**3)**p)**2), x)

________________________________________________________________________________________