Optimal. Leaf size=19 \[ \frac {2 x^{7/2}}{7}+\frac {2 x^{3/2}}{3} \]
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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} \[ \frac {2 x^{7/2}}{7}+\frac {2 x^{3/2}}{3} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \sqrt {x} \left (1+x^2\right ) \, dx &=\int \left (\sqrt {x}+x^{5/2}\right ) \, dx\\ &=\frac {2 x^{3/2}}{3}+\frac {2 x^{7/2}}{7}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 0.84 \[ \frac {2}{21} x^{3/2} \left (3 x^2+7\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 14, normalized size = 0.74 \[ \frac {2}{21} \, {\left (3 \, x^{3} + 7 \, x\right )} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.11, size = 11, normalized size = 0.58 \[ \frac {2}{7} \, x^{\frac {7}{2}} + \frac {2}{3} \, x^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.68 \[ \frac {2 \left (3 x^{2}+7\right ) x^{\frac {3}{2}}}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 11, normalized size = 0.58 \[ \frac {2}{7} \, x^{\frac {7}{2}} + \frac {2}{3} \, x^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 12, normalized size = 0.63 \[ \frac {2\,x^{3/2}\,\left (3\,x^2+7\right )}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.09, size = 15, normalized size = 0.79 \[ \frac {2 x^{\frac {7}{2}}}{7} + \frac {2 x^{\frac {3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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