\(\int \frac {x^3}{\log ^2(c (d+e x^3)^p)} \, dx\) [153]

Optimal result

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

[Out]

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

[In]

Int[x^3/Log[c*(d + e*x^3)^p]^2,x]

[Out]

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

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

Mathematica [N/A]

Not integrable

Time = 0.21 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {x^3}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\int \frac {x^3}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx \]

[In]

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

[Out]

Integrate[x^3/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

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

[In]

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

[Out]

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

[In]

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

[Out]

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

Sympy [N/A]

Not integrable

Time = 15.32 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int \frac {x^3}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\int \frac {x^{3}}{\log {\left (c \left (d + e x^{3}\right )^{p} \right )}^{2}}\, dx \]

[In]

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

[Out]

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

Maxima [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 66, normalized size of antiderivative = 3.67 \[ \int \frac {x^3}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\int { \frac {x^{3}}{\log \left ({\left (e x^{3} + d\right )}^{p} c\right )^{2}} \,d x } \]

[In]

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

[Out]

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

Giac [N/A]

Not integrable

Time = 0.28 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {x^3}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\int { \frac {x^{3}}{\log \left ({\left (e x^{3} + d\right )}^{p} c\right )^{2}} \,d x } \]

[In]

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

[Out]

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

Mupad [N/A]

Not integrable

Time = 1.24 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {x^3}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx=\int \frac {x^3}{{\ln \left (c\,{\left (e\,x^3+d\right )}^p\right )}^2} \,d x \]

[In]

int(x^3/log(c*(d + e*x^3)^p)^2,x)

[Out]

int(x^3/log(c*(d + e*x^3)^p)^2, x)