Optimal. Leaf size=13 \[ \frac {1}{3} (1+2 x)^{3/2} \]
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Rubi [A]
time = 0.01, antiderivative size = 13, normalized size of antiderivative = 1.00, 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}
\begin {gather*} \frac {1}{3} (2 x+1)^{3/2} \end {gather*}
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*}
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Mathematica [A]
time = 0.03, size = 13, normalized size = 1.00 \begin {gather*} \frac {1}{3} (1+2 x)^{3/2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 10, normalized size = 0.77
method | result | size |
gosper | \(\frac {\left (1+2 x \right )^{\frac {3}{2}}}{3}\) | \(10\) |
derivativedivides | \(\frac {\left (1+2 x \right )^{\frac {3}{2}}}{3}\) | \(10\) |
default | \(\frac {\left (1+2 x \right )^{\frac {3}{2}}}{3}\) | \(10\) |
risch | \(\frac {\left (1+2 x \right )^{\frac {3}{2}}}{3}\) | \(10\) |
trager | \(\left (\frac {1}{3}+\frac {2 x}{3}\right ) \sqrt {1+2 x}\) | \(14\) |
meijerg | \(-\frac {\frac {4 \sqrt {\pi }}{3}-\frac {2 \sqrt {\pi }\, \left (2+4 x \right ) \sqrt {1+2 x}}{3}}{4 \sqrt {\pi }}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 2.75, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{3} \, {\left (2 \, x + 1\right )}^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.58, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{3} \, {\left (2 \, x + 1\right )}^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 8, normalized size = 0.62 \begin {gather*} \frac {\left (2 x + 1\right )^{\frac {3}{2}}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.72, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{3} \, {\left (2 \, x + 1\right )}^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.32, size = 9, normalized size = 0.69 \begin {gather*} \frac {{\left (2\,x+1\right )}^{3/2}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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