Optimal. Leaf size=25 \[ \text {Int}\left (\frac {x^4}{\left (a^2 c x^2+c\right )^2 \tan ^{-1}(a x)},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.07, 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 = {} \[ \int \frac {x^4}{\left (c+a^2 c x^2\right )^2 \tan ^{-1}(a x)} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {x^4}{\left (c+a^2 c x^2\right )^2 \tan ^{-1}(a x)} \, dx &=\int \frac {x^4}{\left (c+a^2 c x^2\right )^2 \tan ^{-1}(a x)} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 4.25, size = 0, normalized size = 0.00 \[ \int \frac {x^4}{\left (c+a^2 c x^2\right )^2 \tan ^{-1}(a x)} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.39, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {x^{4}}{{\left (a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right )} \arctan \left (a x\right )}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \mathit {sage}_{0} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 1.01, size = 0, normalized size = 0.00 \[ \int \frac {x^{4}}{\left (a^{2} c \,x^{2}+c \right )^{2} \arctan \left (a x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{4}}{{\left (a^{2} c x^{2} + c\right )}^{2} \arctan \left (a x\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {x^4}{\mathrm {atan}\left (a\,x\right )\,{\left (c\,a^2\,x^2+c\right )}^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \frac {\int \frac {x^{4}}{a^{4} x^{4} \operatorname {atan}{\left (a x \right )} + 2 a^{2} x^{2} \operatorname {atan}{\left (a x \right )} + \operatorname {atan}{\left (a x \right )}}\, dx}{c^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________