Optimal. Leaf size=14 \[ \frac {2 \sqrt {c+d x}}{d} \]
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Rubi [A]
time = 0.00, antiderivative size = 14, 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 \sqrt {c+d x}}{d} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {c+d x}} \, dx &=\frac {2 \sqrt {c+d x}}{d}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 14, normalized size = 1.00 \begin {gather*} \frac {2 \sqrt {c+d x}}{d} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 13, normalized size = 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 | \(\frac {2 \sqrt {d x +c}}{d}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 12, normalized size = 0.86 \begin {gather*} \frac {2 \, \sqrt {d x + c}}{d} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.93, size = 12, normalized size = 0.86 \begin {gather*} \frac {2 \, \sqrt {d x + c}}{d} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 10, normalized size = 0.71 \begin {gather*} \frac {2 \sqrt {c + d x}}{d} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.63, size = 12, normalized size = 0.86 \begin {gather*} \frac {2 \, \sqrt {d x + c}}{d} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 12, normalized size = 0.86 \begin {gather*} \frac {2\,\sqrt {c+d\,x}}{d} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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