Optimal. Leaf size=33 \[ \frac{1}{6} x^6 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{9} b B x^9 \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0325437, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {444, 43} \[ \frac{1}{6} x^6 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{9} b B x^9 \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 444
Rule 43
Rubi steps
\begin{align*} \int x^2 \left (a+b x^3\right ) \left (A+B x^3\right ) \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int (a+b x) (A+B x) \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (a A+(A b+a B) x+b B x^2\right ) \, dx,x,x^3\right )\\ &=\frac{1}{3} a A x^3+\frac{1}{6} (A b+a B) x^6+\frac{1}{9} b B x^9\\ \end{align*}
Mathematica [A] time = 0.0084485, size = 33, normalized size = 1. \[ \frac{1}{6} x^6 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{9} b B x^9 \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 28, normalized size = 0.9 \begin{align*}{\frac{aA{x}^{3}}{3}}+{\frac{ \left ( Ab+Ba \right ){x}^{6}}{6}}+{\frac{bB{x}^{9}}{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.21202, size = 36, normalized size = 1.09 \begin{align*} \frac{1}{9} \, B b x^{9} + \frac{1}{6} \,{\left (B a + A b\right )} x^{6} + \frac{1}{3} \, A a x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.22531, size = 74, normalized size = 2.24 \begin{align*} \frac{1}{9} x^{9} b B + \frac{1}{6} x^{6} a B + \frac{1}{6} x^{6} b A + \frac{1}{3} x^{3} a A \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.059812, size = 29, normalized size = 0.88 \begin{align*} \frac{A a x^{3}}{3} + \frac{B b x^{9}}{9} + x^{6} \left (\frac{A b}{6} + \frac{B a}{6}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.18944, size = 39, normalized size = 1.18 \begin{align*} \frac{1}{9} \, B b x^{9} + \frac{1}{6} \, B a x^{6} + \frac{1}{6} \, A b x^{6} + \frac{1}{3} \, A a x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]