Optimal. Leaf size=19 \[ \text {Int}\left (\frac {x}{\log ^2\left (c \left (d+e x^3\right )^p\right )},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {x}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {x}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx &=\int \frac {x}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.50, size = 0, normalized size = 0.00 \[ \int \frac {x}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.41, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {x}{\log \left ({\left (e x^{3} + d\right )}^{p} c\right )^{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x}{\log \left ({\left (e x^{3} + d\right )}^{p} c\right )^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 4.05, size = 0, normalized size = 0.00 \[ \int \frac {x}{\ln \left (c \left (e \,x^{3}+d \right )^{p}\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {e x^{3} + d}{3 \, {\left (e p x \log \left ({\left (e x^{3} + d\right )}^{p}\right ) + e p x \log \relax (c)\right )}} + \int \frac {2 \, e x^{3} - d}{3 \, {\left (e p x^{2} \log \left ({\left (e x^{3} + d\right )}^{p}\right ) + e p x^{2} \log \relax (c)\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {x}{{\ln \left (c\,{\left (e\,x^3+d\right )}^p\right )}^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x}{\log {\left (c \left (d + e x^{3}\right )^{p} \right )}^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________