Optimal. Leaf size=14 \[ \frac {1}{6} \tan ^{-1}\left (\frac {1}{3} \left (x^2+1\right )\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.214, Rules used = {1107, 618, 204} \[ \frac {1}{6} \tan ^{-1}\left (\frac {1}{3} \left (x^2+1\right )\right ) \]
Antiderivative was successfully verified.
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Rule 204
Rule 618
Rule 1107
Rubi steps
\begin {align*} \int \frac {x}{10+2 x^2+x^4} \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {1}{10+2 x+x^2} \, dx,x,x^2\right )\\ &=-\operatorname {Subst}\left (\int \frac {1}{-36-x^2} \, dx,x,2 \left (1+x^2\right )\right )\\ &=\frac {1}{6} \tan ^{-1}\left (\frac {1}{3} \left (1+x^2\right )\right )\\ \end {align*}
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Mathematica [A] time = 0.01, size = 14, normalized size = 1.00 \[ \frac {1}{6} \tan ^{-1}\left (\frac {1}{3} \left (x^2+1\right )\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 10, normalized size = 0.71 \[ \frac {1}{6} \, \arctan \left (\frac {1}{3} \, x^{2} + \frac {1}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.59, size = 10, normalized size = 0.71 \[ \frac {1}{6} \, \arctan \left (\frac {1}{3} \, x^{2} + \frac {1}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 11, normalized size = 0.79 \[ \frac {\arctan \left (\frac {x^{2}}{3}+\frac {1}{3}\right )}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 2.92, size = 10, normalized size = 0.71 \[ \frac {1}{6} \, \arctan \left (\frac {1}{3} \, x^{2} + \frac {1}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 10, normalized size = 0.71 \[ \frac {\mathrm {atan}\left (\frac {x^2}{3}+\frac {1}{3}\right )}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 10, normalized size = 0.71 \[ \frac {\operatorname {atan}{\left (\frac {x^{2}}{3} + \frac {1}{3} \right )}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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