\(\int \frac {1}{x^2 \log ^2(c (d+e x^3)^p)} \, dx\) [156]

Optimal result

Integrand size = 18, antiderivative size = 18 \[ \int \frac {1}{x^2 \log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\text {Int}\left (\frac {1}{x^2 \log ^2\left (c \left (d+e x^3\right )^p\right )},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {1}{x^2 \log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\int \frac {1}{x^2 \log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx \]

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

Mathematica [N/A]

Not integrable

Time = 0.71 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {1}{x^2 \log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\int \frac {1}{x^2 \log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx \]

[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]

Maple [N/A]

Not integrable

Time = 0.00 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00

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

[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)

Fricas [N/A]

Not integrable

Time = 0.31 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {1}{x^2 \log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\int { \frac {1}{x^{2} \log \left ({\left (e x^{3} + d\right )}^{p} c\right )^{2}} \,d x } \]

[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)

Sympy [N/A]

Not integrable

Time = 22.47 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06 \[ \int \frac {1}{x^2 \log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\int \frac {1}{x^{2} \log {\left (c \left (d + e x^{3}\right )^{p} \right )}^{2}}\, dx \]

[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)

Maxima [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 79, normalized size of antiderivative = 4.39 \[ \int \frac {1}{x^2 \log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\int { \frac {1}{x^{2} \log \left ({\left (e x^{3} + d\right )}^{p} c\right )^{2}} \,d x } \]

[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)

Giac [N/A]

Not integrable

Time = 0.30 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {1}{x^2 \log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\int { \frac {1}{x^{2} \log \left ({\left (e x^{3} + d\right )}^{p} c\right )^{2}} \,d x } \]

[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)

Mupad [N/A]

Not integrable

Time = 1.23 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {1}{x^2 \log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\int \frac {1}{x^2\,{\ln \left (c\,{\left (e\,x^3+d\right )}^p\right )}^2} \,d x \]

[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)