\(\int \frac {f+g x^3}{\log (c (d+e x^2)^p)} \, dx\) [303]

Optimal result

Integrand size = 22, antiderivative size = 22 \[ \int \frac {f+g x^3}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx=\text {Int}\left (\frac {f+g x^3}{\log \left (c \left (d+e x^2\right )^p\right )},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 22, 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 = {} \[ \int \frac {f+g x^3}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int \frac {f+g x^3}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx \]

[In]

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

[Out]

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

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

Mathematica [N/A]

Not integrable

Time = 0.14 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {f+g x^3}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int \frac {f+g x^3}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx \]

[In]

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

[Out]

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

Maple [N/A]

Not integrable

Time = 0.05 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.28 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {f+g x^3}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int { \frac {g x^{3} + f}{\log \left ({\left (e x^{2} + d\right )}^{p} c\right )} \,d x } \]

[In]

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

[Out]

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

Sympy [N/A]

Not integrable

Time = 5.66 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.86 \[ \int \frac {f+g x^3}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int \frac {f + g x^{3}}{\log {\left (c \left (d + e x^{2}\right )^{p} \right )}}\, dx \]

[In]

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

[Out]

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

Maxima [N/A]

Not integrable

Time = 0.30 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {f+g x^3}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int { \frac {g x^{3} + f}{\log \left ({\left (e x^{2} + d\right )}^{p} c\right )} \,d x } \]

[In]

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

[Out]

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

Giac [N/A]

Not integrable

Time = 0.30 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {f+g x^3}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int { \frac {g x^{3} + f}{\log \left ({\left (e x^{2} + d\right )}^{p} c\right )} \,d x } \]

[In]

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

[Out]

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

Mupad [N/A]

Not integrable

Time = 1.44 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {f+g x^3}{\log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int \frac {g\,x^3+f}{\ln \left (c\,{\left (e\,x^2+d\right )}^p\right )} \,d x \]

[In]

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

[Out]

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