Optimal. Leaf size=25 \[ c d^2 x+c d e x^2+\frac{1}{3} c e^2 x^3 \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0058733, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ c d^2 x+c d e x^2+\frac{1}{3} c e^2 x^3 \]
Antiderivative was successfully verified.
[In]
[Out]
Rubi steps
\begin{align*} \int \left (c d^2+2 c d e x+c e^2 x^2\right ) \, dx &=c d^2 x+c d e x^2+\frac{1}{3} c e^2 x^3\\ \end{align*}
Mathematica [A] time = 0.0000363, size = 25, normalized size = 1. \[ c d^2 x+c d e x^2+\frac{1}{3} c e^2 x^3 \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.038, size = 24, normalized size = 1. \begin{align*} c{d}^{2}x+cde{x}^{2}+{\frac{c{e}^{2}{x}^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.01181, size = 31, normalized size = 1.24 \begin{align*} \frac{1}{3} \, c e^{2} x^{3} + c d e x^{2} + c d^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.52701, size = 50, normalized size = 2. \begin{align*} \frac{1}{3} x^{3} e^{2} c + x^{2} e d c + x d^{2} c \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.068721, size = 24, normalized size = 0.96 \begin{align*} c d^{2} x + c d e x^{2} + \frac{c e^{2} x^{3}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.13855, size = 31, normalized size = 1.24 \begin{align*} \frac{1}{3} \, c x^{3} e^{2} + c d x^{2} e + c d^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]