Optimal. Leaf size=8 \[ \frac {1}{2} \sin ^{-1}\left (x^2\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {275, 216} \[ \frac {1}{2} \sin ^{-1}\left (x^2\right ) \]
Antiderivative was successfully verified.
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Rule 216
Rule 275
Rubi steps
\begin {align*} \int \frac {x}{\sqrt {1-x^4}} \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {1}{\sqrt {1-x^2}} \, dx,x,x^2\right )\\ &=\frac {1}{2} \sin ^{-1}\left (x^2\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 8, normalized size = 1.00 \[ \frac {1}{2} \sin ^{-1}\left (x^2\right ) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.82, size = 18, normalized size = 2.25 \[ -\arctan \left (\frac {\sqrt {-x^{4} + 1} - 1}{x^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 6, normalized size = 0.75 \[ \frac {1}{2} \, \arcsin \left (x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 7, normalized size = 0.88 \[ \frac {\arcsin \left (x^{2}\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 2.86, size = 16, normalized size = 2.00 \[ -\frac {1}{2} \, \arctan \left (\frac {\sqrt {-x^{4} + 1}}{x^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.16, size = 16, normalized size = 2.00 \[ \frac {\mathrm {atan}\left (\frac {x^2}{\sqrt {1-x^4}}\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.80, size = 19, normalized size = 2.38 \[ \begin {cases} - \frac {i \operatorname {acosh}{\left (x^{2} \right )}}{2} & \text {for}\: \left |{x^{4}}\right | > 1 \\\frac {\operatorname {asin}{\left (x^{2} \right )}}{2} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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