Optimal. Leaf size=13 \[ \frac{1}{3} (2 x+1)^{3/2} \]
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Rubi [A] time = 0.0009888, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {32} \[ \frac{1}{3} (2 x+1)^{3/2} \]
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin{align*} \int \sqrt{1+2 x} \, dx &=\frac{1}{3} (1+2 x)^{3/2}\\ \end{align*}
Mathematica [A] time = 0.0371224, size = 13, normalized size = 1. \[ \frac{1}{3} (2 x+1)^{3/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.011, size = 10, normalized size = 0.8 \begin{align*}{\frac{1}{3} \left ( 1+2\,x \right ) ^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.944664, size = 12, normalized size = 0.92 \begin{align*} \frac{1}{3} \,{\left (2 \, 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 = 0.416858, size = 28, normalized size = 2.15 \begin{align*} \frac{1}{3} \,{\left (2 \, 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 = 0.051242, size = 8, normalized size = 0.62 \begin{align*} \frac{\left (2 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 = 1.06262, size = 12, normalized size = 0.92 \begin{align*} \frac{1}{3} \,{\left (2 \, x + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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