Optimal. Leaf size=39 \[ \frac{2}{9} x^{9/2} (a B+A b)+\frac{2}{7} a A x^{7/2}+\frac{2}{11} b B x^{11/2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0136939, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {76} \[ \frac{2}{9} x^{9/2} (a B+A b)+\frac{2}{7} a A x^{7/2}+\frac{2}{11} b B x^{11/2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 76
Rubi steps
\begin{align*} \int x^{5/2} (a+b x) (A+B x) \, dx &=\int \left (a A x^{5/2}+(A b+a B) x^{7/2}+b B x^{9/2}\right ) \, dx\\ &=\frac{2}{7} a A x^{7/2}+\frac{2}{9} (A b+a B) x^{9/2}+\frac{2}{11} b B x^{11/2}\\ \end{align*}
Mathematica [A] time = 0.0090589, size = 33, normalized size = 0.85 \[ \frac{2}{693} x^{7/2} (11 a (9 A+7 B x)+7 b x (11 A+9 B x)) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 28, normalized size = 0.7 \begin{align*}{\frac{126\,bB{x}^{2}+154\,Abx+154\,Bax+198\,Aa}{693}{x}^{{\frac{7}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.13839, size = 36, normalized size = 0.92 \begin{align*} \frac{2}{11} \, B b x^{\frac{11}{2}} + \frac{2}{7} \, A a x^{\frac{7}{2}} + \frac{2}{9} \,{\left (B a + A b\right )} x^{\frac{9}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 2.45249, size = 84, normalized size = 2.15 \begin{align*} \frac{2}{693} \,{\left (63 \, B b x^{5} + 99 \, A a x^{3} + 77 \,{\left (B a + A b\right )} x^{4}\right )} \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 3.84029, size = 46, normalized size = 1.18 \begin{align*} \frac{2 A a x^{\frac{7}{2}}}{7} + \frac{2 A b x^{\frac{9}{2}}}{9} + \frac{2 B a x^{\frac{9}{2}}}{9} + \frac{2 B b x^{\frac{11}{2}}}{11} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.17749, size = 39, normalized size = 1. \begin{align*} \frac{2}{11} \, B b x^{\frac{11}{2}} + \frac{2}{9} \, B a x^{\frac{9}{2}} + \frac{2}{9} \, A b x^{\frac{9}{2}} + \frac{2}{7} \, A a x^{\frac{7}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]