Optimal. Leaf size=17 \[ \frac{(d+e x)^3}{3 c e} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0047593, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {27, 12, 32} \[ \frac{(d+e x)^3}{3 c e} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 27
Rule 12
Rule 32
Rubi steps
\begin{align*} \int \frac{(d+e x)^4}{c d^2+2 c d e x+c e^2 x^2} \, dx &=\int \frac{(d+e x)^2}{c} \, dx\\ &=\frac{\int (d+e x)^2 \, dx}{c}\\ &=\frac{(d+e x)^3}{3 c e}\\ \end{align*}
Mathematica [A] time = 0.0008047, size = 17, normalized size = 1. \[ \frac{(d+e x)^3}{3 c e} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.039, size = 16, normalized size = 0.9 \begin{align*}{\frac{ \left ( ex+d \right ) ^{3}}{3\,ce}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.10039, size = 35, normalized size = 2.06 \begin{align*} \frac{e^{2} x^{3} + 3 \, d e x^{2} + 3 \, d^{2} x}{3 \, c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.92547, size = 53, normalized size = 3.12 \begin{align*} \frac{e^{2} x^{3} + 3 \, d e x^{2} + 3 \, d^{2} x}{3 \, c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 0.117196, size = 24, normalized size = 1.41 \begin{align*} \frac{d^{2} x}{c} + \frac{d e x^{2}}{c} + \frac{e^{2} x^{3}}{3 c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: NotImplementedError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]