Optimal. Leaf size=13 \[ \frac{1}{3} \left (x^2+1\right )^{3/2} \]
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Rubi [A] time = 0.0019663, 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} \[ \frac{1}{3} \left (x^2+1\right )^{3/2} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x \sqrt{1+x^2} \, dx &=\frac{1}{3} \left (1+x^2\right )^{3/2}\\ \end{align*}
Mathematica [A] time = 0.0003708, size = 13, normalized size = 1. \[ \frac{1}{3} \left (x^2+1\right )^{3/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 10, normalized size = 0.8 \begin{align*}{\frac{1}{3} \left ({x}^{2}+1 \right ) ^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.930322, size = 12, normalized size = 0.92 \begin{align*} \frac{1}{3} \,{\left (x^{2} + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.70136, size = 28, normalized size = 2.15 \begin{align*} \frac{1}{3} \,{\left (x^{2} + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.179528, size = 22, normalized size = 1.69 \begin{align*} \frac{x^{2} \sqrt{x^{2} + 1}}{3} + \frac{\sqrt{x^{2} + 1}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05952, size = 12, normalized size = 0.92 \begin{align*} \frac{1}{3} \,{\left (x^{2} + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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