Optimal. Leaf size=16 \[ \sqrt {1-x^2}+x \sin ^{-1}(x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 1.000, Rules used = {4619, 261} \[ \sqrt {1-x^2}+x \sin ^{-1}(x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 261
Rule 4619
Rubi steps
\begin {align*} \int \sin ^{-1}(x) \, dx &=x \sin ^{-1}(x)-\int \frac {x}{\sqrt {1-x^2}} \, dx\\ &=\sqrt {1-x^2}+x \sin ^{-1}(x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ \sqrt {1-x^2}+x \sin ^{-1}(x) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.45, size = 14, normalized size = 0.88 \[ x \arcsin \relax (x) + \sqrt {-x^{2} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.05, size = 14, normalized size = 0.88 \[ x \arcsin \relax (x) + \sqrt {-x^{2} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 15, normalized size = 0.94 \[ x \arcsin \relax (x )+\sqrt {-x^{2}+1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.01, size = 14, normalized size = 0.88 \[ x \arcsin \relax (x) + \sqrt {-x^{2} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.00, size = 14, normalized size = 0.88 \[ x\,\mathrm {asin}\relax (x)+\sqrt {1-x^2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.13, size = 12, normalized size = 0.75 \[ x \operatorname {asin}{\relax (x )} + \sqrt {1 - x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________