Optimal. Leaf size=11 \[ x-\frac {2 x^{3/2}}{3} \]
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Rubi [A]
time = 0.01, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 3, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {1412, 26, 45}
\begin {gather*} x-\frac {2 x^{3/2}}{3} \end {gather*}
Antiderivative was successfully verified.
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Rule 26
Rule 45
Rule 1412
Rubi steps
\begin {align*} \int \frac {1-x}{1+\sqrt {x}} \, dx &=2 \text {Subst}\left (\int \frac {x \left (1-x^2\right )}{1+x} \, dx,x,\sqrt {x}\right )\\ &=2 \text {Subst}\left (\int (1-x) x \, dx,x,\sqrt {x}\right )\\ &=2 \text {Subst}\left (\int \left (x-x^2\right ) \, dx,x,\sqrt {x}\right )\\ &=x-\frac {2 x^{3/2}}{3}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} x-\frac {2 x^{3/2}}{3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.52, size = 8, normalized size = 0.73
method | result | size |
derivativedivides | \(x -\frac {2 x^{\frac {3}{2}}}{3}\) | \(8\) |
default | \(x -\frac {2 x^{\frac {3}{2}}}{3}\) | \(8\) |
trager | \(-1+x -\frac {2 x^{\frac {3}{2}}}{3}\) | \(9\) |
meijerg | \(2 \sqrt {x}-\frac {\sqrt {x}\, \left (4 x -6 \sqrt {x}+12\right )}{6}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 7, normalized size = 0.64 \begin {gather*} -\frac {2}{3} \, x^{\frac {3}{2}} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 7, normalized size = 0.64 \begin {gather*} -\frac {2}{3} \, x^{\frac {3}{2}} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 8, normalized size = 0.73 \begin {gather*} - \frac {2 x^{\frac {3}{2}}}{3} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.50, size = 7, normalized size = 0.64 \begin {gather*} -\frac {2}{3} \, x^{\frac {3}{2}} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 7, normalized size = 0.64 \begin {gather*} x-\frac {2\,x^{3/2}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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