Optimal. Leaf size=39 \[ \frac {2}{13} x^{13/2} (A c+b B)+\frac {2}{11} A b x^{11/2}+\frac {2}{15} B c x^{15/2} \]
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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} \[ \frac {2}{13} x^{13/2} (A c+b B)+\frac {2}{11} A b x^{11/2}+\frac {2}{15} B c x^{15/2} \]
Antiderivative was successfully verified.
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Rule 765
Rubi steps
\begin {align*} \int x^{7/2} (A+B x) \left (b x+c x^2\right ) \, dx &=\int \left (A b x^{9/2}+(b B+A c) x^{11/2}+B c x^{13/2}\right ) \, dx\\ &=\frac {2}{11} A b x^{11/2}+\frac {2}{13} (b B+A c) x^{13/2}+\frac {2}{15} B c x^{15/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 33, normalized size = 0.85 \[ \frac {2 x^{11/2} (15 A (13 b+11 c x)+11 B x (15 b+13 c x))}{2145} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 32, normalized size = 0.82 \[ \frac {2}{2145} \, {\left (143 \, B c x^{7} + 195 \, A b x^{5} + 165 \, {\left (B b + A c\right )} x^{6}\right )} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 29, normalized size = 0.74 \[ \frac {2}{15} \, B c x^{\frac {15}{2}} + \frac {2}{13} \, B b x^{\frac {13}{2}} + \frac {2}{13} \, A c x^{\frac {13}{2}} + \frac {2}{11} \, A b x^{\frac {11}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 28, normalized size = 0.72 \[ \frac {2 \left (143 B c \,x^{2}+165 A c x +165 B b x +195 A b \right ) x^{\frac {11}{2}}}{2145} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 27, normalized size = 0.69 \[ \frac {2}{15} \, B c x^{\frac {15}{2}} + \frac {2}{11} \, A b x^{\frac {11}{2}} + \frac {2}{13} \, {\left (B b + A c\right )} x^{\frac {13}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 27, normalized size = 0.69 \[ \frac {2\,x^{11/2}\,\left (195\,A\,b+165\,A\,c\,x+165\,B\,b\,x+143\,B\,c\,x^2\right )}{2145} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 7.89, size = 46, normalized size = 1.18 \[ \frac {2 A b x^{\frac {11}{2}}}{11} + \frac {2 A c x^{\frac {13}{2}}}{13} + \frac {2 B b x^{\frac {13}{2}}}{13} + \frac {2 B c x^{\frac {15}{2}}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
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