Optimal. Leaf size=15 \[ \frac {1}{4} \sqrt {4 x^2+9} \]
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Rubi [A] time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {261} \[ \frac {1}{4} \sqrt {4 x^2+9} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int \frac {x}{\sqrt {9+4 x^2}} \, dx &=\frac {1}{4} \sqrt {9+4 x^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ \frac {1}{4} \sqrt {4 x^2+9} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 11, normalized size = 0.73 \[ \frac {1}{4} \, \sqrt {4 \, x^{2} + 9} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.12, size = 11, normalized size = 0.73 \[ \frac {1}{4} \, \sqrt {4 \, x^{2} + 9} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 12, normalized size = 0.80 \[ \frac {\sqrt {4 x^{2}+9}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 11, normalized size = 0.73 \[ \frac {1}{4} \, \sqrt {4 \, x^{2} + 9} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 9, normalized size = 0.60 \[ \frac {\sqrt {x^2+\frac {9}{4}}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 10, normalized size = 0.67 \[ \frac {\sqrt {4 x^{2} + 9}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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