Optimal. Leaf size=11 \[ x-\frac{2 x^{3/2}}{3} \]
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Rubi [A] time = 0.008115, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {1398, 26, 43} \[ x-\frac{2 x^{3/2}}{3} \]
Antiderivative was successfully verified.
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Rule 1398
Rule 26
Rule 43
Rubi steps
\begin{align*} \int \frac{1-x}{1+\sqrt{x}} \, dx &=2 \operatorname{Subst}\left (\int \frac{x \left (1-x^2\right )}{1+x} \, dx,x,\sqrt{x}\right )\\ &=2 \operatorname{Subst}\left (\int (1-x) x \, dx,x,\sqrt{x}\right )\\ &=2 \operatorname{Subst}\left (\int \left (x-x^2\right ) \, dx,x,\sqrt{x}\right )\\ &=x-\frac{2 x^{3/2}}{3}\\ \end{align*}
Mathematica [A] time = 0.000415, size = 11, normalized size = 1. \[ x-\frac{2 x^{3/2}}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 8, normalized size = 0.7 \begin{align*} x-{\frac{2}{3}{x}^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.28941, size = 9, normalized size = 0.82 \begin{align*} -\frac{2}{3} \, x^{\frac{3}{2}} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.45331, size = 24, normalized size = 2.18 \begin{align*} -\frac{2}{3} \, x^{\frac{3}{2}} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.13158, size = 8, normalized size = 0.73 \begin{align*} - \frac{2 x^{\frac{3}{2}}}{3} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16135, size = 9, normalized size = 0.82 \begin{align*} -\frac{2}{3} \, x^{\frac{3}{2}} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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