Optimal. Leaf size=22 \[ \frac {b \tan ^{-1}\left (\sqrt {\frac {3}{2}} x^2\right )}{2 \sqrt {6}} \]
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Rubi [A] time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {12, 275, 203} \[ \frac {b \tan ^{-1}\left (\sqrt {\frac {3}{2}} x^2\right )}{2 \sqrt {6}} \]
Antiderivative was successfully verified.
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Rule 12
Rule 203
Rule 275
Rubi steps
\begin {align*} \int \frac {b x}{2+3 x^4} \, dx &=b \int \frac {x}{2+3 x^4} \, dx\\ &=\frac {1}{2} b \operatorname {Subst}\left (\int \frac {1}{2+3 x^2} \, dx,x,x^2\right )\\ &=\frac {b \tan ^{-1}\left (\sqrt {\frac {3}{2}} x^2\right )}{2 \sqrt {6}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 1.00 \[ \frac {b \tan ^{-1}\left (\sqrt {\frac {3}{2}} x^2\right )}{2 \sqrt {6}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.78, size = 15, normalized size = 0.68 \[ \frac {1}{12} \, \sqrt {6} b \arctan \left (\frac {1}{2} \, \sqrt {6} x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 15, normalized size = 0.68 \[ \frac {1}{12} \, \sqrt {6} b \arctan \left (\frac {1}{2} \, \sqrt {6} x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 16, normalized size = 0.73 \[ \frac {\sqrt {6}\, b \arctan \left (\frac {\sqrt {6}\, x^{2}}{2}\right )}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 2.88, size = 15, normalized size = 0.68 \[ \frac {1}{12} \, \sqrt {6} b \arctan \left (\frac {1}{2} \, \sqrt {6} x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.77, size = 15, normalized size = 0.68 \[ \frac {\sqrt {6}\,b\,\mathrm {atan}\left (\frac {\sqrt {6}\,x^2}{2}\right )}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 19, normalized size = 0.86 \[ \frac {\sqrt {6} b \operatorname {atan}{\left (\frac {\sqrt {6} x^{2}}{2} \right )}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
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