Optimal. Leaf size=16 \[ -\frac{1}{6 b \left (a+b x^2\right )^3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0049299, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {28, 261} \[ -\frac{1}{6 b \left (a+b x^2\right )^3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 28
Rule 261
Rubi steps
\begin{align*} \int \frac{x}{\left (a^2+2 a b x^2+b^2 x^4\right )^2} \, dx &=b^4 \int \frac{x}{\left (a b+b^2 x^2\right )^4} \, dx\\ &=-\frac{1}{6 b \left (a+b x^2\right )^3}\\ \end{align*}
Mathematica [A] time = 0.002448, size = 16, normalized size = 1. \[ -\frac{1}{6 b \left (a+b x^2\right )^3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.046, size = 15, normalized size = 0.9 \begin{align*} -{\frac{1}{6\,b \left ( b{x}^{2}+a \right ) ^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] time = 0.977073, size = 50, normalized size = 3.12 \begin{align*} -\frac{1}{6 \,{\left (b^{4} x^{6} + 3 \, a b^{3} x^{4} + 3 \, a^{2} b^{2} x^{2} + a^{3} b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.76343, size = 73, normalized size = 4.56 \begin{align*} -\frac{1}{6 \,{\left (b^{4} x^{6} + 3 \, a b^{3} x^{4} + 3 \, a^{2} b^{2} x^{2} + a^{3} b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 0.540938, size = 39, normalized size = 2.44 \begin{align*} - \frac{1}{6 a^{3} b + 18 a^{2} b^{2} x^{2} + 18 a b^{3} x^{4} + 6 b^{4} x^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.11452, size = 19, normalized size = 1.19 \begin{align*} -\frac{1}{6 \,{\left (b x^{2} + a\right )}^{3} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]