Integrand size = 9, antiderivative size = 16 \[ \int \sqrt {a+b x} \, dx=\frac {2 (a+b x)^{3/2}}{3 b} \]
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Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {32} \[ \int \sqrt {a+b x} \, dx=\frac {2 (a+b x)^{3/2}}{3 b} \]
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Rule 32
Rubi steps \begin{align*} \text {integral}& = \frac {2 (a+b x)^{3/2}}{3 b} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \sqrt {a+b x} \, dx=\frac {2 (a+b x)^{3/2}}{3 b} \]
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Time = 0.09 (sec) , antiderivative size = 13, normalized size of antiderivative = 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 | \(\frac {2 \left (b x +a \right )^{\frac {3}{2}}}{3 b}\) | \(13\) |
pseudoelliptic | \(\frac {2 \left (b x +a \right )^{\frac {3}{2}}}{3 b}\) | \(13\) |
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none
Time = 0.23 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \sqrt {a+b x} \, dx=\frac {2 \, {\left (b x + a\right )}^{\frac {3}{2}}}{3 \, b} \]
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Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \sqrt {a+b x} \, dx=\frac {2 \left (a + b x\right )^{\frac {3}{2}}}{3 b} \]
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none
Time = 0.20 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \sqrt {a+b x} \, dx=\frac {2 \, {\left (b x + a\right )}^{\frac {3}{2}}}{3 \, b} \]
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none
Time = 0.28 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \sqrt {a+b x} \, dx=\frac {2 \, {\left (b x + a\right )}^{\frac {3}{2}}}{3 \, b} \]
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Time = 0.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.75 \[ \int \sqrt {a+b x} \, dx=\frac {2\,{\left (a+b\,x\right )}^{3/2}}{3\,b} \]
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