Optimal. Leaf size=39 \[ \frac{2}{13} x^{13/2} (a B+A b)+\frac{2}{7} a A x^{7/2}+\frac{2}{19} b B x^{19/2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0158456, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {448} \[ \frac{2}{13} x^{13/2} (a B+A b)+\frac{2}{7} a A x^{7/2}+\frac{2}{19} b B x^{19/2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 448
Rubi steps
\begin{align*} \int x^{5/2} \left (a+b x^3\right ) \left (A+B x^3\right ) \, dx &=\int \left (a A x^{5/2}+(A b+a B) x^{11/2}+b B x^{17/2}\right ) \, dx\\ &=\frac{2}{7} a A x^{7/2}+\frac{2}{13} (A b+a B) x^{13/2}+\frac{2}{19} b B x^{19/2}\\ \end{align*}
Mathematica [A] time = 0.0138206, size = 33, normalized size = 0.85 \[ \frac{2 x^{7/2} \left (133 x^3 (a B+A b)+247 a A+91 b B x^6\right )}{1729} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 32, normalized size = 0.8 \begin{align*}{\frac{182\,bB{x}^{6}+266\,A{x}^{3}b+266\,B{x}^{3}a+494\,Aa}{1729}{x}^{{\frac{7}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.934875, size = 36, normalized size = 0.92 \begin{align*} \frac{2}{19} \, B b x^{\frac{19}{2}} + \frac{2}{13} \,{\left (B a + A b\right )} x^{\frac{13}{2}} + \frac{2}{7} \, A a x^{\frac{7}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.44092, size = 88, normalized size = 2.26 \begin{align*} \frac{2}{1729} \,{\left (91 \, B b x^{9} + 133 \,{\left (B a + A b\right )} x^{6} + 247 \, A a x^{3}\right )} \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 17.5613, size = 46, normalized size = 1.18 \begin{align*} \frac{2 A a x^{\frac{7}{2}}}{7} + \frac{2 A b x^{\frac{13}{2}}}{13} + \frac{2 B a x^{\frac{13}{2}}}{13} + \frac{2 B b x^{\frac{19}{2}}}{19} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.10463, size = 39, normalized size = 1. \begin{align*} \frac{2}{19} \, B b x^{\frac{19}{2}} + \frac{2}{13} \, B a x^{\frac{13}{2}} + \frac{2}{13} \, A b x^{\frac{13}{2}} + \frac{2}{7} \, A a x^{\frac{7}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]