Optimal. Leaf size=16 \[ \sqrt{1-x^2}+x \sin ^{-1}(x) \]
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Rubi [A] time = 0.0038397, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 2, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 1., Rules used = {4619, 261} \[ \sqrt{1-x^2}+x \sin ^{-1}(x) \]
Antiderivative was successfully verified.
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Rule 4619
Rule 261
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 = 0.0020695, size = 16, normalized size = 1. \[ \sqrt{1-x^2}+x \sin ^{-1}(x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 15, normalized size = 0.9 \begin{align*} x\arcsin \left ( x \right ) +\sqrt{-{x}^{2}+1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.40238, size = 19, normalized size = 1.19 \begin{align*} x \arcsin \left (x\right ) + \sqrt{-x^{2} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.02459, size = 41, normalized size = 2.56 \begin{align*} x \arcsin \left (x\right ) + \sqrt{-x^{2} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.11681, size = 12, normalized size = 0.75 \begin{align*} x \operatorname{asin}{\left (x \right )} + \sqrt{1 - x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06511, size = 19, normalized size = 1.19 \begin{align*} x \arcsin \left (x\right ) + \sqrt{-x^{2} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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