Optimal. Leaf size=27 \[ \text {Int}\left (\frac {x^m \left (a^2 c x^2+c\right )^2}{\tan ^{-1}(a x)^{3/2}},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.05, 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 = {} \[ \int \frac {x^m \left (c+a^2 c x^2\right )^2}{\tan ^{-1}(a x)^{3/2}} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {x^m \left (c+a^2 c x^2\right )^2}{\tan ^{-1}(a x)^{3/2}} \, dx &=\int \frac {x^m \left (c+a^2 c x^2\right )^2}{\tan ^{-1}(a x)^{3/2}} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 1.50, size = 0, normalized size = 0.00 \[ \int \frac {x^m \left (c+a^2 c x^2\right )^2}{\tan ^{-1}(a x)^{3/2}} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.55, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (a^{4} c^{2} x^{4} + 2 \, a^{2} c^{2} x^{2} + c^{2}\right )} x^{m}}{\arctan \left (a x\right )^{\frac {3}{2}}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \mathit {sage}_{0} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 4.21, size = 0, normalized size = 0.00 \[ \int \frac {x^{m} \left (a^{2} c \,x^{2}+c \right )^{2}}{\arctan \left (a x \right )^{\frac {3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: RuntimeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {x^m\,{\left (c\,a^2\,x^2+c\right )}^2}{{\mathrm {atan}\left (a\,x\right )}^{3/2}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ c^{2} \left (\int \frac {x^{m}}{\operatorname {atan}^{\frac {3}{2}}{\left (a x \right )}}\, dx + \int \frac {2 a^{2} x^{2} x^{m}}{\operatorname {atan}^{\frac {3}{2}}{\left (a x \right )}}\, dx + \int \frac {a^{4} x^{4} x^{m}}{\operatorname {atan}^{\frac {3}{2}}{\left (a x \right )}}\, dx\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________