\(\int \frac {1}{\log ^2(c (d+e x^3)^p)} \, dx\) [155]

Optimal result

Integrand size = 14, antiderivative size = 14 \[ \int \frac {1}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\text {Int}\left (\frac {1}{\log ^2\left (c \left (d+e x^3\right )^p\right )},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.00 (sec) , antiderivative size = 14, 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 = {} \[ \int \frac {1}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\int \frac {1}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx \]

[In]

Int[Log[c*(d + e*x^3)^p]^(-2),x]

[Out]

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

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

Mathematica [N/A]

Not integrable

Time = 0.17 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {1}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\int \frac {1}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx \]

[In]

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

[Out]

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

Maple [N/A]

Not integrable

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.29 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {1}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\int { \frac {1}{\log \left ({\left (e x^{3} + d\right )}^{p} c\right )^{2}} \,d x } \]

[In]

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

[Out]

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

Sympy [N/A]

Not integrable

Time = 9.05 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.07 \[ \int \frac {1}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\int \frac {1}{\log {\left (c \left (d + e x^{3}\right )^{p} \right )}^{2}}\, dx \]

[In]

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

[Out]

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

Maxima [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 77, normalized size of antiderivative = 5.50 \[ \int \frac {1}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\int { \frac {1}{\log \left ({\left (e x^{3} + d\right )}^{p} c\right )^{2}} \,d x } \]

[In]

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

[Out]

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

Giac [N/A]

Not integrable

Time = 0.29 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {1}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\int { \frac {1}{\log \left ({\left (e x^{3} + d\right )}^{p} c\right )^{2}} \,d x } \]

[In]

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

[Out]

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

Mupad [N/A]

Not integrable

Time = 1.18 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {1}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\int \frac {1}{{\ln \left (c\,{\left (e\,x^3+d\right )}^p\right )}^2} \,d x \]

[In]

int(1/log(c*(d + e*x^3)^p)^2,x)

[Out]

int(1/log(c*(d + e*x^3)^p)^2, x)