Integrand size = 9, antiderivative size = 14 \[ \int \frac {1}{\sqrt {c+d x}} \, dx=\frac {2 \sqrt {c+d x}}{d} \]
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Time = 0.00 (sec) , antiderivative size = 14, 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} \[ \int \frac {1}{\sqrt {c+d x}} \, dx=\frac {2 \sqrt {c+d x}}{d} \]
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Rule 32
Rubi steps \begin{align*} \text {integral}& = \frac {2 \sqrt {c+d x}}{d} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {1}{\sqrt {c+d x}} \, dx=\frac {2 \sqrt {c+d x}}{d} \]
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Time = 0.22 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.93
method | result | size |
gosper | \(\frac {2 \sqrt {d x +c}}{d}\) | \(13\) |
derivativedivides | \(\frac {2 \sqrt {d x +c}}{d}\) | \(13\) |
default | \(\frac {2 \sqrt {d x +c}}{d}\) | \(13\) |
trager | \(\frac {2 \sqrt {d x +c}}{d}\) | \(13\) |
risch | \(\frac {2 \sqrt {d x +c}}{d}\) | \(13\) |
pseudoelliptic | \(\frac {2 \sqrt {d x +c}}{d}\) | \(13\) |
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none
Time = 0.23 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {1}{\sqrt {c+d x}} \, dx=\frac {2 \, \sqrt {d x + c}}{d} \]
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Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \frac {1}{\sqrt {c+d x}} \, dx=\frac {2 \sqrt {c + d x}}{d} \]
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none
Time = 0.20 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {1}{\sqrt {c+d x}} \, dx=\frac {2 \, \sqrt {d x + c}}{d} \]
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none
Time = 0.32 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {1}{\sqrt {c+d x}} \, dx=\frac {2 \, \sqrt {d x + c}}{d} \]
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Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {1}{\sqrt {c+d x}} \, dx=\frac {2\,\sqrt {c+d\,x}}{d} \]
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