Optimal. Leaf size=16 \[ \frac{\left (a+b x^2\right )^9}{18 b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0023727, 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} \[ \frac{\left (a+b x^2\right )^9}{18 b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 261
Rubi steps
\begin{align*} \int x \left (a+b x^2\right )^8 \, dx &=\frac{\left (a+b x^2\right )^9}{18 b}\\ \end{align*}
Mathematica [A] time = 0.0018185, size = 16, normalized size = 1. \[ \frac{\left (a+b x^2\right )^9}{18 b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] time = 0., size = 91, normalized size = 5.7 \begin{align*}{\frac{{b}^{8}{x}^{18}}{18}}+{\frac{a{b}^{7}{x}^{16}}{2}}+2\,{a}^{2}{b}^{6}{x}^{14}+{\frac{14\,{a}^{3}{b}^{5}{x}^{12}}{3}}+7\,{a}^{4}{b}^{4}{x}^{10}+7\,{a}^{5}{b}^{3}{x}^{8}+{\frac{14\,{a}^{6}{b}^{2}{x}^{6}}{3}}+2\,{a}^{7}b{x}^{4}+{\frac{{a}^{8}{x}^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 2.53358, size = 19, normalized size = 1.19 \begin{align*} \frac{{\left (b x^{2} + a\right )}^{9}}{18 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.32205, size = 201, normalized size = 12.56 \begin{align*} \frac{1}{18} x^{18} b^{8} + \frac{1}{2} x^{16} b^{7} a + 2 x^{14} b^{6} a^{2} + \frac{14}{3} x^{12} b^{5} a^{3} + 7 x^{10} b^{4} a^{4} + 7 x^{8} b^{3} a^{5} + \frac{14}{3} x^{6} b^{2} a^{6} + 2 x^{4} b a^{7} + \frac{1}{2} x^{2} a^{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 0.078476, size = 99, normalized size = 6.19 \begin{align*} \frac{a^{8} x^{2}}{2} + 2 a^{7} b x^{4} + \frac{14 a^{6} b^{2} x^{6}}{3} + 7 a^{5} b^{3} x^{8} + 7 a^{4} b^{4} x^{10} + \frac{14 a^{3} b^{5} x^{12}}{3} + 2 a^{2} b^{6} x^{14} + \frac{a b^{7} x^{16}}{2} + \frac{b^{8} x^{18}}{18} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.67879, size = 19, normalized size = 1.19 \begin{align*} \frac{{\left (b x^{2} + a\right )}^{9}}{18 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]