Optimal. Leaf size=17 \[ x-\sqrt {1-x^2} \sin ^{-1}(x) \]
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Rubi [A] time = 0.03, antiderivative size = 17, normalized size of antiderivative = 1.00, 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 8
Rule 4677
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*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 1.00 \[ x-\sqrt {1-x^2} \sin ^{-1}(x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 15, normalized size = 0.88 \[ -\sqrt {-x^{2} + 1} \arcsin \relax (x) + x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.85, size = 15, normalized size = 0.88 \[ -\sqrt {-x^{2} + 1} \arcsin \relax (x) + x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 16, normalized size = 0.94 \[ x -\sqrt {-x^{2}+1}\, \arcsin \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.96, size = 15, normalized size = 0.88 \[ -\sqrt {-x^{2} + 1} \arcsin \relax (x) + x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {x\,\mathrm {asin}\relax (x)}{\sqrt {1-x^2}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 12, normalized size = 0.71 \[ x - \sqrt {1 - x^{2}} \operatorname {asin}{\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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