Optimal. Leaf size=16 \[ \frac {2 (a+b x)^{3/2}}{3 b} \]
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Rubi [A]
time = 0.00, antiderivative size = 16, 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 {2 (a+b x)^{3/2}}{3 b} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int \sqrt {a+b x} \, dx &=\frac {2 (a+b x)^{3/2}}{3 b}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 16, normalized size = 1.00 \begin {gather*} \frac {2 (a+b x)^{3/2}}{3 b} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 13, normalized size = 0.81
method | result | size |
gosper | \(\frac {2 \left (b x +a \right )^{\frac {3}{2}}}{3 b}\) | \(13\) |
derivativedivides | \(\frac {2 \left (b x +a \right )^{\frac {3}{2}}}{3 b}\) | \(13\) |
default | \(\frac {2 \left (b x +a \right )^{\frac {3}{2}}}{3 b}\) | \(13\) |
trager | \(\frac {2 \left (b x +a \right )^{\frac {3}{2}}}{3 b}\) | \(13\) |
risch | \(\frac {2 \left (b x +a \right )^{\frac {3}{2}}}{3 b}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.22, size = 12, normalized size = 0.75 \begin {gather*} \frac {2 \, {\left (b x + a\right )}^{\frac {3}{2}}}{3 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.51, size = 12, normalized size = 0.75 \begin {gather*} \frac {2 \, {\left (b x + a\right )}^{\frac {3}{2}}}{3 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 12, normalized size = 0.75 \begin {gather*} \frac {2 \left (a + b x\right )^{\frac {3}{2}}}{3 b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.46, size = 12, normalized size = 0.75 \begin {gather*} \frac {2 \, {\left (b x + a\right )}^{\frac {3}{2}}}{3 \, b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 12, normalized size = 0.75 \begin {gather*} \frac {2\,{\left (a+b\,x\right )}^{3/2}}{3\,b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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