Optimal. Leaf size=27 \[ \text {Int}\left (\frac {1}{\left (f+g x^2\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )},x\right ) \]
[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 = {} \[ \int \frac {1}{\left (f+g x^2\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {1}{\left (f+g x^2\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx &=\int \frac {1}{\left (f+g x^2\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 7.73, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (f+g x^2\right )^2 \log ^2\left (c \left (d+e x^2\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.62, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{{\left (g^{2} x^{4} + 2 \, f g x^{2} + f^{2}\right )} \log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (g x^{2} + f\right )}^{2} \log \left ({\left (e x^{2} + d\right )}^{p} c\right )^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 4.73, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (g \,x^{2}+f \right )^{2} \ln \left (c \left (e \,x^{2}+d \right )^{p}\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {e x^{2} + d}{2 \, {\left (e g^{2} p x^{5} \log \relax (c) + 2 \, e f g p x^{3} \log \relax (c) + e f^{2} p x \log \relax (c) + {\left (e g^{2} p^{2} x^{5} + 2 \, e f g p^{2} x^{3} + e f^{2} p^{2} x\right )} \log \left (e x^{2} + d\right )\right )}} - \int \frac {3 \, e g x^{4} - {\left (e f - 5 \, d g\right )} x^{2} + d f}{2 \, {\left (e g^{3} p x^{8} \log \relax (c) + 3 \, e f g^{2} p x^{6} \log \relax (c) + 3 \, e f^{2} g p x^{4} \log \relax (c) + e f^{3} p x^{2} \log \relax (c) + {\left (e g^{3} p^{2} x^{8} + 3 \, e f g^{2} p^{2} x^{6} + 3 \, e f^{2} g p^{2} x^{4} + e f^{3} p^{2} x^{2}\right )} \log \left (e x^{2} + d\right )\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {1}{{\ln \left (c\,{\left (e\,x^2+d\right )}^p\right )}^2\,{\left (g\,x^2+f\right )}^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________