Optimal. Leaf size=11 \[ \frac{2}{3} (x+1)^{3/2} \]
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Rubi [A] time = 0.0006516, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {32} \[ \frac{2}{3} (x+1)^{3/2} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin{align*} \int \sqrt{1+x} \, dx &=\frac{2}{3} (1+x)^{3/2}\\ \end{align*}
Mathematica [A] time = 0.0021514, size = 11, normalized size = 1. \[ \frac{2}{3} (x+1)^{3/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 8, normalized size = 0.7 \begin{align*}{\frac{2}{3} \left ( 1+x \right ) ^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.992441, size = 9, normalized size = 0.82 \begin{align*} \frac{2}{3} \,{\left (x + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.41257, size = 26, normalized size = 2.36 \begin{align*} \frac{2}{3} \,{\left (x + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.051079, size = 8, normalized size = 0.73 \begin{align*} \frac{2 \left (x + 1\right )^{\frac{3}{2}}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10494, size = 9, normalized size = 0.82 \begin{align*} \frac{2}{3} \,{\left (x + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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