Optimal. Leaf size=39 \[ \frac {2}{7} x^{7/2} (A c+b B)+\frac {2}{5} A b x^{5/2}+\frac {2}{9} B c x^{9/2} \]
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Rubi [A] time = 0.02, antiderivative size = 39, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {765} \[ \frac {2}{7} x^{7/2} (A c+b B)+\frac {2}{5} A b x^{5/2}+\frac {2}{9} B c x^{9/2} \]
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin {align*} \int \sqrt {x} (A+B x) \left (b x+c x^2\right ) \, dx &=\int \left (A b x^{3/2}+(b B+A c) x^{5/2}+B c x^{7/2}\right ) \, dx\\ &=\frac {2}{5} A b x^{5/2}+\frac {2}{7} (b B+A c) x^{7/2}+\frac {2}{9} B c x^{9/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 33, normalized size = 0.85 \[ \frac {2}{315} x^{5/2} (9 A (7 b+5 c x)+5 B x (9 b+7 c x)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.99, size = 32, normalized size = 0.82 \[ \frac {2}{315} \, {\left (35 \, B c x^{4} + 63 \, A b x^{2} + 45 \, {\left (B b + A c\right )} x^{3}\right )} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 29, normalized size = 0.74 \[ \frac {2}{9} \, B c x^{\frac {9}{2}} + \frac {2}{7} \, B b x^{\frac {7}{2}} + \frac {2}{7} \, A c x^{\frac {7}{2}} + \frac {2}{5} \, A b x^{\frac {5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 28, normalized size = 0.72 \[ \frac {2 \left (35 B c \,x^{2}+45 A c x +45 B b x +63 A b \right ) x^{\frac {5}{2}}}{315} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 27, normalized size = 0.69 \[ \frac {2}{9} \, B c x^{\frac {9}{2}} + \frac {2}{5} \, A b x^{\frac {5}{2}} + \frac {2}{7} \, {\left (B b + A c\right )} x^{\frac {7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 27, normalized size = 0.69 \[ \frac {2\,x^{5/2}\,\left (63\,A\,b+45\,A\,c\,x+45\,B\,b\,x+35\,B\,c\,x^2\right )}{315} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.33, size = 37, normalized size = 0.95 \[ \frac {2 A b x^{\frac {5}{2}}}{5} + \frac {2 B c x^{\frac {9}{2}}}{9} + \frac {2 x^{\frac {7}{2}} \left (A c + B b\right )}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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