Optimal. Leaf size=16 \[ \frac{\left (a+b x^2\right )^3}{6 b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0022917, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {261} \[ \frac{\left (a+b x^2\right )^3}{6 b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 261
Rubi steps
\begin{align*} \int x \left (a+b x^2\right )^2 \, dx &=\frac{\left (a+b x^2\right )^3}{6 b}\\ \end{align*}
Mathematica [A] time = 0.0017881, size = 16, normalized size = 1. \[ \frac{\left (a+b x^2\right )^3}{6 b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0., size = 25, normalized size = 1.6 \begin{align*}{\frac{{b}^{2}{x}^{6}}{6}}+{\frac{ab{x}^{4}}{2}}+{\frac{{a}^{2}{x}^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 2.24358, size = 19, normalized size = 1.19 \begin{align*} \frac{{\left (b x^{2} + a\right )}^{3}}{6 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.24651, size = 55, normalized size = 3.44 \begin{align*} \frac{1}{6} x^{6} b^{2} + \frac{1}{2} x^{4} b a + \frac{1}{2} x^{2} a^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 0.059924, size = 24, normalized size = 1.5 \begin{align*} \frac{a^{2} x^{2}}{2} + \frac{a b x^{4}}{2} + \frac{b^{2} x^{6}}{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.27716, size = 19, normalized size = 1.19 \begin{align*} \frac{{\left (b x^{2} + a\right )}^{3}}{6 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]