Optimal. Leaf size=13 \[ \frac {1}{3} \left (x^2+1\right )^{3/2} \]
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Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \[ \frac {1}{3} \left (x^2+1\right )^{3/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 9, normalized size = 0.69 \[ \frac {1}{3} \, {\left (x^{2} + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 9, normalized size = 0.69 \[ \frac {1}{3} \, {\left (x^{2} + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 10, normalized size = 0.77 \[ \frac {\left (x^{2}+1\right )^{\frac {3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 9, normalized size = 0.69 \[ \frac {1}{3} \, {\left (x^{2} + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 9, normalized size = 0.69 \[ \frac {{\left (x^2+1\right )}^{3/2}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.20, size = 22, normalized size = 1.69 \[ \frac {x^{2} \sqrt {x^{2} + 1}}{3} + \frac {\sqrt {x^{2} + 1}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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