Optimal. Leaf size=24 \[ \text {Int}\left (\frac {\left (c+a^2 c x^2\right )^3}{\sqrt {\text {ArcTan}(a x)}},x\right ) \]
[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 = {}
\begin {gather*} \int \frac {\left (c+a^2 c x^2\right )^3}{\sqrt {\text {ArcTan}(a x)}} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\left (c+a^2 c x^2\right )^3}{\sqrt {\tan ^{-1}(a x)}} \, dx &=\int \frac {\left (c+a^2 c x^2\right )^3}{\sqrt {\tan ^{-1}(a x)}} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.53, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (c+a^2 c x^2\right )^3}{\sqrt {\text {ArcTan}(a x)}} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 1.19, size = 0, normalized size = 0.00 \[\int \frac {\left (a^{2} c \,x^{2}+c \right )^{3}}{\sqrt {\arctan \left (a x \right )}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} c^{3} \left (\int \frac {3 a^{2} x^{2}}{\sqrt {\operatorname {atan}{\left (a x \right )}}}\, dx + \int \frac {3 a^{4} x^{4}}{\sqrt {\operatorname {atan}{\left (a x \right )}}}\, dx + \int \frac {a^{6} x^{6}}{\sqrt {\operatorname {atan}{\left (a x \right )}}}\, dx + \int \frac {1}{\sqrt {\operatorname {atan}{\left (a x \right )}}}\, dx\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\left (c\,a^2\,x^2+c\right )}^3}{\sqrt {\mathrm {atan}\left (a\,x\right )}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________