Optimal. Leaf size=16 \[ \frac{\left (a x^2+b\right )^3}{6 a} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.004456, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {263, 261} \[ \frac{\left (a x^2+b\right )^3}{6 a} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 263
Rule 261
Rubi steps
\begin{align*} \int \left (a+\frac{b}{x^2}\right )^2 x^5 \, dx &=\int x \left (b+a x^2\right )^2 \, dx\\ &=\frac{\left (b+a x^2\right )^3}{6 a}\\ \end{align*}
Mathematica [A] time = 0.0020138, size = 16, normalized size = 1. \[ \frac{\left (a x^2+b\right )^3}{6 a} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0., size = 25, normalized size = 1.6 \begin{align*}{\frac{{a}^{2}{x}^{6}}{6}}+{\frac{ab{x}^{4}}{2}}+{\frac{{b}^{2}{x}^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.949848, size = 32, normalized size = 2. \begin{align*} \frac{1}{6} \, a^{2} x^{6} + \frac{1}{2} \, a b x^{4} + \frac{1}{2} \, b^{2} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.32867, size = 55, normalized size = 3.44 \begin{align*} \frac{1}{6} \, a^{2} x^{6} + \frac{1}{2} \, a b x^{4} + \frac{1}{2} \, b^{2} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 0.060206, size = 24, normalized size = 1.5 \begin{align*} \frac{a^{2} x^{6}}{6} + \frac{a b x^{4}}{2} + \frac{b^{2} x^{2}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.18804, size = 32, normalized size = 2. \begin{align*} \frac{1}{6} \, a^{2} x^{6} + \frac{1}{2} \, a b x^{4} + \frac{1}{2} \, b^{2} x^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]