Optimal. Leaf size=20 \[ \text {Int}\left (\frac {1-a^2 x^2}{\tanh ^{-1}(a x)},x\right ) \]
[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 = {} \[ \int \frac {1-a^2 x^2}{\tanh ^{-1}(a x)} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {1-a^2 x^2}{\tanh ^{-1}(a x)} \, dx &=\int \frac {1-a^2 x^2}{\tanh ^{-1}(a x)} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.34, size = 0, normalized size = 0.00 \[ \int \frac {1-a^2 x^2}{\tanh ^{-1}(a x)} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.70, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {a^{2} x^{2} - 1}{\operatorname {artanh}\left (a x\right )}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int -\frac {a^{2} x^{2} - 1}{\operatorname {artanh}\left (a x\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.62, size = 0, normalized size = 0.00 \[ \int \frac {-a^{2} x^{2}+1}{\arctanh \left (a x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ -\int \frac {a^{2} x^{2} - 1}{\operatorname {artanh}\left (a x\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ -\int \frac {a^2\,x^2-1}{\mathrm {atanh}\left (a\,x\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ - \int \frac {a^{2} x^{2}}{\operatorname {atanh}{\left (a x \right )}}\, dx - \int \left (- \frac {1}{\operatorname {atanh}{\left (a x \right )}}\right )\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________