Optimal. Leaf size=26 \[ \text {Int}\left (\frac {1}{x^2 \sqrt {a^2 x^2+1} \sinh ^{-1}(a x)},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.10, 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 = {} \[ \int \frac {1}{x^2 \sqrt {1+a^2 x^2} \sinh ^{-1}(a x)} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {1}{x^2 \sqrt {1+a^2 x^2} \sinh ^{-1}(a x)} \, dx &=\int \frac {1}{x^2 \sqrt {1+a^2 x^2} \sinh ^{-1}(a x)} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.75, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^2 \sqrt {1+a^2 x^2} \sinh ^{-1}(a x)} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.43, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sqrt {a^{2} x^{2} + 1}}{{\left (a^{2} x^{4} + x^{2}\right )} \operatorname {arsinh}\left (a x\right )}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {a^{2} x^{2} + 1} x^{2} \operatorname {arsinh}\left (a x\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.21, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{2} \arcsinh \left (a x \right ) \sqrt {a^{2} x^{2}+1}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {a^{2} x^{2} + 1} x^{2} \operatorname {arsinh}\left (a x\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {1}{x^2\,\mathrm {asinh}\left (a\,x\right )\,\sqrt {a^2\,x^2+1}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{2} \sqrt {a^{2} x^{2} + 1} \operatorname {asinh}{\left (a x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________