Optimal. Leaf size=16 \[ -\frac{1}{18 b \left (a+b x^2\right )^9} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0027757, 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} \[ -\frac{1}{18 b \left (a+b x^2\right )^9} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 261
Rubi steps
\begin{align*} \int \frac{x}{\left (a+b x^2\right )^{10}} \, dx &=-\frac{1}{18 b \left (a+b x^2\right )^9}\\ \end{align*}
Mathematica [A] time = 0.0023917, size = 16, normalized size = 1. \[ -\frac{1}{18 b \left (a+b x^2\right )^9} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0., size = 15, normalized size = 0.9 \begin{align*} -{\frac{1}{18\,b \left ( b{x}^{2}+a \right ) ^{9}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 2.24934, size = 19, normalized size = 1.19 \begin{align*} -\frac{1}{18 \,{\left (b x^{2} + a\right )}^{9} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.23636, size = 223, normalized size = 13.94 \begin{align*} -\frac{1}{18 \,{\left (b^{10} x^{18} + 9 \, a b^{9} x^{16} + 36 \, a^{2} b^{8} x^{14} + 84 \, a^{3} b^{7} x^{12} + 126 \, a^{4} b^{6} x^{10} + 126 \, a^{5} b^{5} x^{8} + 84 \, a^{6} b^{4} x^{6} + 36 \, a^{7} b^{3} x^{4} + 9 \, a^{8} b^{2} x^{2} + a^{9} b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 7.01308, size = 110, normalized size = 6.88 \begin{align*} - \frac{1}{18 a^{9} b + 162 a^{8} b^{2} x^{2} + 648 a^{7} b^{3} x^{4} + 1512 a^{6} b^{4} x^{6} + 2268 a^{5} b^{5} x^{8} + 2268 a^{4} b^{6} x^{10} + 1512 a^{3} b^{7} x^{12} + 648 a^{2} b^{8} x^{14} + 162 a b^{9} x^{16} + 18 b^{10} x^{18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.06648, size = 19, normalized size = 1.19 \begin{align*} -\frac{1}{18 \,{\left (b x^{2} + a\right )}^{9} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]