Optimal. Leaf size=21 \[ \log (x)-\frac {\sqrt {1-x^2} \sin ^{-1}(x)}{x} \]
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Rubi [A] time = 0.04, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {4681, 29} \[ \log (x)-\frac {\sqrt {1-x^2} \sin ^{-1}(x)}{x} \]
Antiderivative was successfully verified.
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Rule 29
Rule 4681
Rubi steps
\begin {align*} \int \frac {\sin ^{-1}(x)}{x^2 \sqrt {1-x^2}} \, dx &=-\frac {\sqrt {1-x^2} \sin ^{-1}(x)}{x}+\int \frac {1}{x} \, dx\\ &=-\frac {\sqrt {1-x^2} \sin ^{-1}(x)}{x}+\log (x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 21, normalized size = 1.00 \[ \log (x)-\frac {\sqrt {1-x^2} \sin ^{-1}(x)}{x} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 22, normalized size = 1.05 \[ \frac {x \log \relax (x) - \sqrt {-x^{2} + 1} \arcsin \relax (x)}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.03, size = 40, normalized size = 1.90 \[ \frac {1}{2} \, {\left (\frac {x}{\sqrt {-x^{2} + 1} - 1} - \frac {\sqrt {-x^{2} + 1} - 1}{x}\right )} \arcsin \relax (x) + \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 20, normalized size = 0.95 \[ \ln \relax (x )-\frac {\sqrt {-x^{2}+1}\, \arcsin \relax (x )}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.94, size = 19, normalized size = 0.90 \[ -\frac {\sqrt {-x^{2} + 1} \arcsin \relax (x)}{x} + \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {\mathrm {asin}\relax (x)}{x^2\,\sqrt {1-x^2}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {asin}{\relax (x )}}{x^{2} \sqrt {- \left (x - 1\right ) \left (x + 1\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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