Optimal. Leaf size=9 \[ 2 \sqrt {1+x} \]
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Rubi [A]
time = 0.00, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {32}
\begin {gather*} 2 \sqrt {x+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {1+x}} \, dx &=2 \sqrt {1+x}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} 2 \sqrt {1+x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.54, size = 8, normalized size = 0.89
method | result | size |
gosper | \(2 \sqrt {1+x}\) | \(8\) |
derivativedivides | \(2 \sqrt {1+x}\) | \(8\) |
default | \(2 \sqrt {1+x}\) | \(8\) |
trager | \(2 \sqrt {1+x}\) | \(8\) |
risch | \(2 \sqrt {1+x}\) | \(8\) |
meijerg | \(\frac {-2 \sqrt {\pi }+2 \sqrt {\pi }\, \sqrt {1+x}}{\sqrt {\pi }}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 7, normalized size = 0.78 \begin {gather*} 2 \, \sqrt {x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.32, size = 7, normalized size = 0.78 \begin {gather*} 2 \, \sqrt {x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 7, normalized size = 0.78 \begin {gather*} 2 \sqrt {x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.85, size = 7, normalized size = 0.78 \begin {gather*} 2 \, \sqrt {x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.09, size = 7, normalized size = 0.78 \begin {gather*} 2\,\sqrt {x+1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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