Optimal. Leaf size=20 \[ d x+\frac {e x^2}{2}+\frac {f x^3}{3} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 20, normalized size of antiderivative = 1.00, 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 = {1600}
\begin {gather*} d x+\frac {e x^2}{2}+\frac {f x^3}{3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 1600
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 = 0.00, size = 20, normalized size = 1.00 \begin {gather*} d x+\frac {e x^2}{2}+\frac {f x^3}{3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.01, size = 17, normalized size = 0.85
method | result | size |
default | \(d x +\frac {1}{2} e \,x^{2}+\frac {1}{3} f \,x^{3}\) | \(17\) |
norman | \(d x +\frac {1}{2} e \,x^{2}+\frac {1}{3} f \,x^{3}\) | \(17\) |
risch | \(d x +\frac {1}{2} e \,x^{2}+\frac {1}{3} f \,x^{3}\) | \(17\) |
gosper | \(\frac {x \left (2 f \,x^{2}+3 e x +6 d \right )}{6}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 17, normalized size = 0.85 \begin {gather*} \frac {1}{3} \, f x^{3} + \frac {1}{2} \, x^{2} e + d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.39, size = 16, normalized size = 0.80 \begin {gather*} \frac {1}{3} \, f x^{3} + \frac {1}{2} \, e x^{2} + d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.02, size = 15, normalized size = 0.75 \begin {gather*} d x + \frac {e x^{2}}{2} + \frac {f x^{3}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 4.05, size = 17, normalized size = 0.85 \begin {gather*} \frac {1}{3} \, f x^{3} + \frac {1}{2} \, x^{2} e + d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.03, size = 16, normalized size = 0.80 \begin {gather*} \frac {f\,x^3}{3}+\frac {e\,x^2}{2}+d\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________