Optimal. Leaf size=13 \[ -\frac{1}{3 \left (x^2+4\right )^{3/2}} \]
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Rubi [A] time = 0.0020326, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {261} \[ -\frac{1}{3 \left (x^2+4\right )^{3/2}} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x}{\left (4+x^2\right )^{5/2}} \, dx &=-\frac{1}{3 \left (4+x^2\right )^{3/2}}\\ \end{align*}
Mathematica [A] time = 0.0021071, size = 13, normalized size = 1. \[ -\frac{1}{3 \left (x^2+4\right )^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 10, normalized size = 0.8 \begin{align*} -{\frac{1}{3} \left ({x}^{2}+4 \right ) ^{-{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.920904, size = 12, normalized size = 0.92 \begin{align*} -\frac{1}{3 \,{\left (x^{2} + 4\right )}^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 2.36814, size = 53, normalized size = 4.08 \begin{align*} -\frac{\sqrt{x^{2} + 4}}{3 \,{\left (x^{4} + 8 \, x^{2} + 16\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 2.32755, size = 26, normalized size = 2. \begin{align*} - \frac{1}{3 x^{2} \sqrt{x^{2} + 4} + 12 \sqrt{x^{2} + 4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05664, size = 12, normalized size = 0.92 \begin{align*} -\frac{1}{3 \,{\left (x^{2} + 4\right )}^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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