Optimal. Leaf size=19 \[ \frac {2 x^{5/2}}{5}+\frac {2 x^{3/2}}{3} \]
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Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14} \[ \frac {2 x^{5/2}}{5}+\frac {2 x^{3/2}}{3} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {x+x^2}{\sqrt {x}} \, dx &=\int \left (\sqrt {x}+x^{3/2}\right ) \, dx\\ &=\frac {2 x^{3/2}}{3}+\frac {2 x^{5/2}}{5}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 0.74 \[ \frac {2}{15} x^{3/2} (3 x+5) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 14, normalized size = 0.74 \[ \frac {2}{15} \, {\left (3 \, x^{2} + 5 \, x\right )} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.94, size = 11, normalized size = 0.58 \[ \frac {2}{5} \, x^{\frac {5}{2}} + \frac {2}{3} \, x^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 11, normalized size = 0.58 \[ \frac {2 \left (3 x +5\right ) x^{\frac {3}{2}}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 11, normalized size = 0.58 \[ \frac {2}{5} \, x^{\frac {5}{2}} + \frac {2}{3} \, x^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 10, normalized size = 0.53 \[ \frac {2\,x^{3/2}\,\left (3\,x+5\right )}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.22, size = 15, normalized size = 0.79 \[ \frac {2 x^{\frac {5}{2}}}{5} + \frac {2 x^{\frac {3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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