Optimal. Leaf size=27 \[ \frac {1}{10} (2 x+1)^{5/2}-\frac {1}{6} (2 x+1)^{3/2} \]
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Rubi [A] time = 0.00, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {43} \[ \frac {1}{10} (2 x+1)^{5/2}-\frac {1}{6} (2 x+1)^{3/2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int x \sqrt {1+2 x} \, dx &=\int \left (-\frac {1}{2} \sqrt {1+2 x}+\frac {1}{2} (1+2 x)^{3/2}\right ) \, dx\\ &=-\frac {1}{6} (1+2 x)^{3/2}+\frac {1}{10} (1+2 x)^{5/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 0.67 \[ \frac {1}{15} (2 x+1)^{3/2} (3 x-1) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 17, normalized size = 0.63 \[ \frac {1}{15} \, {\left (6 \, x^{2} + x - 1\right )} \sqrt {2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.94, size = 19, normalized size = 0.70 \[ \frac {1}{10} \, {\left (2 \, x + 1\right )}^{\frac {5}{2}} - \frac {1}{6} \, {\left (2 \, x + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.56 \[ \frac {\left (2 x +1\right )^{\frac {3}{2}} \left (3 x -1\right )}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 19, normalized size = 0.70 \[ \frac {1}{10} \, {\left (2 \, x + 1\right )}^{\frac {5}{2}} - \frac {1}{6} \, {\left (2 \, x + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 14, normalized size = 0.52 \[ \frac {{\left (2\,x+1\right )}^{3/2}\,\left (6\,x-2\right )}{30} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.02, size = 36, normalized size = 1.33 \[ \frac {2 x^{2} \sqrt {2 x + 1}}{5} + \frac {x \sqrt {2 x + 1}}{15} - \frac {\sqrt {2 x + 1}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
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