Optimal. Leaf size=17 \[ x-\sqrt{1-x^2} \sin ^{-1}(x) \]
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Rubi [A] time = 0.0284056, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {4677, 8} \[ x-\sqrt{1-x^2} \sin ^{-1}(x) \]
Antiderivative was successfully verified.
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Rule 4677
Rule 8
Rubi steps
\begin{align*} \int \frac{x \sin ^{-1}(x)}{\sqrt{1-x^2}} \, dx &=-\sqrt{1-x^2} \sin ^{-1}(x)+\int 1 \, dx\\ &=x-\sqrt{1-x^2} \sin ^{-1}(x)\\ \end{align*}
Mathematica [A] time = 0.0053169, size = 17, normalized size = 1. \[ x-\sqrt{1-x^2} \sin ^{-1}(x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.044, size = 16, 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 = 1.43044, size = 20, normalized size = 1.18 \begin{align*} -\sqrt{-x^{2} + 1} \arcsin \left (x\right ) + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.47955, size = 42, normalized size = 2.47 \begin{align*} -\sqrt{-x^{2} + 1} \arcsin \left (x\right ) + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.187062, size = 12, normalized size = 0.71 \begin{align*} x - \sqrt{1 - x^{2}} \operatorname{asin}{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12276, size = 20, normalized size = 1.18 \begin{align*} -\sqrt{-x^{2} + 1} \arcsin \left (x\right ) + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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