\(\int \frac {1}{(f+g x^3) \log (c (d+e x^2)^p)} \, dx\) [304]

Optimal result

Integrand size = 24, antiderivative size = 24 \[ \int \frac {1}{\left (f+g x^3\right ) \log \left (c \left (d+e x^2\right )^p\right )} \, dx=\text {Int}\left (\frac {1}{\left (f+g x^3\right ) \log \left (c \left (d+e x^2\right )^p\right )},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.02 (sec) , antiderivative size = 24, 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 = {} \[ \int \frac {1}{\left (f+g x^3\right ) \log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int \frac {1}{\left (f+g x^3\right ) \log \left (c \left (d+e x^2\right )^p\right )} \, dx \]

[In]

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

[Out]

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

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

Mathematica [N/A]

Not integrable

Time = 7.20 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {1}{\left (f+g x^3\right ) \log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int \frac {1}{\left (f+g x^3\right ) \log \left (c \left (d+e x^2\right )^p\right )} \, dx \]

[In]

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

[Out]

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

Maple [N/A]

Not integrable

Time = 0.22 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.30 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {1}{\left (f+g x^3\right ) \log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int { \frac {1}{{\left (g x^{3} + f\right )} \log \left ({\left (e x^{2} + d\right )}^{p} c\right )} \,d x } \]

[In]

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

[Out]

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

Sympy [N/A]

Not integrable

Time = 101.48 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83 \[ \int \frac {1}{\left (f+g x^3\right ) \log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int \frac {1}{\left (f + g x^{3}\right ) \log {\left (c \left (d + e x^{2}\right )^{p} \right )}}\, dx \]

[In]

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

[Out]

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

Maxima [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {1}{\left (f+g x^3\right ) \log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int { \frac {1}{{\left (g x^{3} + f\right )} \log \left ({\left (e x^{2} + d\right )}^{p} c\right )} \,d x } \]

[In]

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

[Out]

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

Giac [N/A]

Not integrable

Time = 0.29 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {1}{\left (f+g x^3\right ) \log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int { \frac {1}{{\left (g x^{3} + f\right )} \log \left ({\left (e x^{2} + d\right )}^{p} c\right )} \,d x } \]

[In]

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

[Out]

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

Mupad [N/A]

Not integrable

Time = 1.68 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.08 \[ \int \frac {1}{\left (f+g x^3\right ) \log \left (c \left (d+e x^2\right )^p\right )} \, dx=\int \frac {1}{\ln \left (c\,{\left (e\,x^2+d\right )}^p\right )\,\left (g\,x^3+f\right )} \,d x \]

[In]

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

[Out]

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