Optimal. Leaf size=55 \[ \frac {2}{5} x^{5/2} (a B+A b)+\frac {2}{3} a A x^{3/2}+\frac {2}{7} x^{7/2} (A c+b B)+\frac {2}{9} B c x^{9/2} \]
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Rubi [A] time = 0.02, antiderivative size = 55, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {765} \[ \frac {2}{5} x^{5/2} (a B+A b)+\frac {2}{3} a A x^{3/2}+\frac {2}{7} x^{7/2} (A c+b B)+\frac {2}{9} B c x^{9/2} \]
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin {align*} \int \sqrt {x} (A+B x) \left (a+b x+c x^2\right ) \, dx &=\int \left (a A \sqrt {x}+(A b+a B) x^{3/2}+(b B+A c) x^{5/2}+B c x^{7/2}\right ) \, dx\\ &=\frac {2}{3} a A x^{3/2}+\frac {2}{5} (A b+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 = 0.04, size = 47, normalized size = 0.85 \[ \frac {2}{315} x^{3/2} (21 a (5 A+3 B x)+x (9 A (7 b+5 c x)+5 B x (9 b+7 c x))) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.47, size = 42, normalized size = 0.76 \[ \frac {2}{315} \, {\left (35 \, B c x^{4} + 45 \, {\left (B b + A c\right )} x^{3} + 105 \, A a x + 63 \, {\left (B a + A b\right )} x^{2}\right )} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 43, normalized size = 0.78 \[ \frac {2}{9} \, B c x^{\frac {9}{2}} + \frac {2}{7} \, B b x^{\frac {7}{2}} + \frac {2}{7} \, A c x^{\frac {7}{2}} + \frac {2}{5} \, B a x^{\frac {5}{2}} + \frac {2}{5} \, A b x^{\frac {5}{2}} + \frac {2}{3} \, A a x^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 42, normalized size = 0.76 \[ \frac {2 \left (35 B c \,x^{3}+45 A c \,x^{2}+45 B b \,x^{2}+63 A b x +63 B a x +105 A a \right ) x^{\frac {3}{2}}}{315} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 39, normalized size = 0.71 \[ \frac {2}{9} \, B c x^{\frac {9}{2}} + \frac {2}{7} \, {\left (B b + A c\right )} x^{\frac {7}{2}} + \frac {2}{3} \, A a x^{\frac {3}{2}} + \frac {2}{5} \, {\left (B a + A b\right )} x^{\frac {5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 41, normalized size = 0.75 \[ x^{5/2}\,\left (\frac {2\,A\,b}{5}+\frac {2\,B\,a}{5}\right )+x^{7/2}\,\left (\frac {2\,A\,c}{7}+\frac {2\,B\,b}{7}\right )+\frac {2\,A\,a\,x^{3/2}}{3}+\frac {2\,B\,c\,x^{9/2}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.79, size = 53, normalized size = 0.96 \[ \frac {2 A a x^{\frac {3}{2}}}{3} + \frac {2 B c x^{\frac {9}{2}}}{9} + \frac {2 x^{\frac {7}{2}} \left (A c + B b\right )}{7} + \frac {2 x^{\frac {5}{2}} \left (A b + B a\right )}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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