Optimal. Leaf size=9 \[ \frac {\log \left (\sin ^{-1}(a x)\right )}{a} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {4639} \[ \frac {\log \left (\sin ^{-1}(a x)\right )}{a} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 4639
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {1-a^2 x^2} \sin ^{-1}(a x)} \, dx &=\frac {\log \left (\sin ^{-1}(a x)\right )}{a}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 9, normalized size = 1.00 \[ \frac {\log \left (\sin ^{-1}(a x)\right )}{a} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 2.44, size = 11, normalized size = 1.22 \[ \frac {\log \left (-\arcsin \left (a x\right )\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.58, size = 10, normalized size = 1.11 \[ \frac {\log \left ({\left | \arcsin \left (a x\right ) \right |}\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 10, normalized size = 1.11 \[ \frac {\ln \left (\arcsin \left (a x \right )\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.43, size = 9, normalized size = 1.00 \[ \frac {\log \left (\arcsin \left (a x\right )\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.15, size = 9, normalized size = 1.00 \[ \frac {\ln \left (\mathrm {asin}\left (a\,x\right )\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.41, size = 7, normalized size = 0.78 \[ \frac {\log {\left (\operatorname {asin}{\left (a x \right )} \right )}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________