Optimal. Leaf size=20 \[ \text {Int}\left (\frac {a^2 c x^2+c}{\tan ^{-1}(a x)^3},x\right ) \]
[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 = {} \[ \int \frac {c+a^2 c x^2}{\tan ^{-1}(a x)^3} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {c+a^2 c x^2}{\tan ^{-1}(a x)^3} \, dx &=\int \frac {c+a^2 c x^2}{\tan ^{-1}(a x)^3} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 1.26, size = 0, normalized size = 0.00 \[ \int \frac {c+a^2 c x^2}{\tan ^{-1}(a x)^3} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.46, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {a^{2} c x^{2} + c}{\arctan \left (a x\right )^{3}}, x\right ) \]
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 = 1.46, size = 0, normalized size = 0.00 \[ \int \frac {a^{2} c \,x^{2}+c}{\arctan \left (a x \right )^{3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {a^{4} c x^{4} + 2 \, a^{2} c x^{2} - 4 \, a \arctan \left (a x\right )^{2} \int \frac {5 \, a^{4} c x^{4} + 6 \, a^{2} c x^{2} + c}{\arctan \left (a x\right )}\,{d x} + 4 \, {\left (a^{5} c x^{5} + 2 \, a^{3} c x^{3} + a c x\right )} \arctan \left (a x\right ) + c}{2 \, a \arctan \left (a x\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {c\,a^2\,x^2+c}{{\mathrm {atan}\left (a\,x\right )}^3} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ c \left (\int \frac {a^{2} x^{2}}{\operatorname {atan}^{3}{\left (a x \right )}}\, dx + \int \frac {1}{\operatorname {atan}^{3}{\left (a x \right )}}\, dx\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________