Optimal. Leaf size=20 \[ d x+\frac{e x^2}{2}+\frac{f x^3}{3} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0331228, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 63, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.016, Rules used = {1586} \[ d x+\frac{e x^2}{2}+\frac{f x^3}{3} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1586
Rubi steps
\begin{align*} \int \frac{a d+a e x+(b d+a f) x^2+b e x^3+(c d+b f) x^4+c e x^5+c f x^6}{a+b x^2+c x^4} \, dx &=\int \left (d+e x+f x^2\right ) \, dx\\ &=d x+\frac{e x^2}{2}+\frac{f x^3}{3}\\ \end{align*}
Mathematica [A] time = 0.0017564, size = 20, normalized size = 1. \[ d x+\frac{e x^2}{2}+\frac{f x^3}{3} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0., size = 17, normalized size = 0.9 \begin{align*} dx+{\frac{e{x}^{2}}{2}}+{\frac{f{x}^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.951129, size = 22, normalized size = 1.1 \begin{align*} \frac{1}{3} \, f x^{3} + \frac{1}{2} \, e x^{2} + d x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.68847, size = 39, normalized size = 1.95 \begin{align*} \frac{1}{3} \, f x^{3} + \frac{1}{2} \, e x^{2} + d x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.079969, size = 15, normalized size = 0.75 \begin{align*} d x + \frac{e x^{2}}{2} + \frac{f x^{3}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.18739, size = 23, normalized size = 1.15 \begin{align*} \frac{1}{3} \, f x^{3} + \frac{1}{2} \, x^{2} e + d x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]