Optimal. Leaf size=26 \[ \text {Int}\left (\frac {1}{x^2 \sqrt {1+a^2 x^2} \sinh ^{-1}(a x)},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.06, 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 {1}{x^2 \sqrt {1+a^2 x^2} \sinh ^{-1}(a x)} \, dx \end {gather*}
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 = 0.10, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x^2 \sqrt {1+a^2 x^2} \sinh ^{-1}(a x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 180.00, 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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [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]
________________________________________________________________________________________
Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x^{2} \sqrt {a^{2} x^{2} + 1} \operatorname {asinh}{\left (a x \right )}}\, dx \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 {1}{x^2\,\mathrm {asinh}\left (a\,x\right )\,\sqrt {a^2\,x^2+1}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________