Optimal. Leaf size=21 \[ \text {Int}\left (\frac {x^2}{\log ^2\left (c \left (a+b x^2\right )^p\right )},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, 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 = {} \[ \int \frac {x^2}{\log ^2\left (c \left (a+b x^2\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {x^2}{\log ^2\left (c \left (a+b x^2\right )^p\right )} \, dx &=\int \frac {x^2}{\log ^2\left (c \left (a+b x^2\right )^p\right )} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.35, size = 0, normalized size = 0.00 \[ \int \frac {x^2}{\log ^2\left (c \left (a+b x^2\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.43, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {x^{2}}{\log \left ({\left (b x^{2} + a\right )}^{p} c\right )^{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{2}}{\log \left ({\left (b x^{2} + a\right )}^{p} c\right )^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 3.52, size = 0, normalized size = 0.00 \[ \int \frac {x^{2}}{\ln \left (c \left (b \,x^{2}+a \right )^{p}\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {b x^{3} + a x}{2 \, {\left (b p^{2} \log \left (b x^{2} + a\right ) + b p \log \relax (c)\right )}} + \int \frac {3 \, b x^{2} + a}{2 \, {\left (b p^{2} \log \left (b x^{2} + a\right ) + b p \log \relax (c)\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {x^2}{{\ln \left (c\,{\left (b\,x^2+a\right )}^p\right )}^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{2}}{\log {\left (c \left (a + b x^{2}\right )^{p} \right )}^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________