Optimal. Leaf size=12 \[ c x+\frac{d x^2}{2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0138278, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.033, Rules used = {1586} \[ c x+\frac{d x^2}{2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1586
Rubi steps
\begin{align*} \int \frac{a c+a d x+b c x^3+b d x^4}{a+b x^3} \, dx &=\int (c+d x) \, dx\\ &=c x+\frac{d x^2}{2}\\ \end{align*}
Mathematica [A] time = 0.0007036, size = 12, normalized size = 1. \[ c x+\frac{d x^2}{2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 11, normalized size = 0.9 \begin{align*} cx+{\frac{d{x}^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.949419, size = 14, normalized size = 1.17 \begin{align*} \frac{1}{2} \, d x^{2} + c x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.25331, size = 23, normalized size = 1.92 \begin{align*} \frac{1}{2} \, d x^{2} + c x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.069176, size = 8, normalized size = 0.67 \begin{align*} c x + \frac{d x^{2}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.06273, size = 14, normalized size = 1.17 \begin{align*} \frac{1}{2} \, d x^{2} + c x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]