Optimal. Leaf size=11 \[ \frac{x}{2 x^2+1} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0053507, antiderivative size = 11, 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, 383} \[ \frac{x}{2 x^2+1} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 28
Rule 383
Rubi steps
\begin{align*} \int \frac{1-2 x^2}{1+4 x^2+4 x^4} \, dx &=4 \int \frac{1-2 x^2}{\left (2+4 x^2\right )^2} \, dx\\ &=\frac{x}{1+2 x^2}\\ \end{align*}
Mathematica [A] time = 0.0047324, size = 11, normalized size = 1. \[ \frac{x}{2 x^2+1} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.046, size = 11, normalized size = 1. \begin{align*}{\frac{x}{2} \left ({x}^{2}+{\frac{1}{2}} \right ) ^{-1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.974697, size = 15, normalized size = 1.36 \begin{align*} \frac{x}{2 \, x^{2} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.23776, size = 20, normalized size = 1.82 \begin{align*} \frac{x}{2 \, x^{2} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.08454, size = 7, normalized size = 0.64 \begin{align*} \frac{x}{2 x^{2} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.14189, size = 15, normalized size = 1.36 \begin{align*} \frac{x}{2 \, x^{2} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]