Optimal. Leaf size=32 \[ 4 a c x+\frac{4 c^2 x^3}{3}+c d x^4+\frac{d^2 x^5}{5} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0058112, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ 4 a c x+\frac{4 c^2 x^3}{3}+c d x^4+\frac{d^2 x^5}{5} \]
Antiderivative was successfully verified.
[In]
[Out]
Rubi steps
\begin{align*} \int \left (4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right ) \, dx &=4 a c x+\frac{4 c^2 x^3}{3}+c d x^4+\frac{d^2 x^5}{5}\\ \end{align*}
Mathematica [A] time = 0.0000498, size = 32, normalized size = 1. \[ 4 a c x+\frac{4 c^2 x^3}{3}+c d x^4+\frac{d^2 x^5}{5} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0., size = 29, normalized size = 0.9 \begin{align*} 4\,acx+{\frac{4\,{c}^{2}{x}^{3}}{3}}+cd{x}^{4}+{\frac{{d}^{2}{x}^{5}}{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.04914, size = 38, normalized size = 1.19 \begin{align*} \frac{1}{5} \, d^{2} x^{5} + c d x^{4} + \frac{4}{3} \, c^{2} x^{3} + 4 \, a c x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.10546, size = 63, normalized size = 1.97 \begin{align*} \frac{1}{5} x^{5} d^{2} + x^{4} d c + \frac{4}{3} x^{3} c^{2} + 4 x c a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.066172, size = 31, normalized size = 0.97 \begin{align*} 4 a c x + \frac{4 c^{2} x^{3}}{3} + c d x^{4} + \frac{d^{2} x^{5}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.11857, size = 38, normalized size = 1.19 \begin{align*} \frac{1}{5} \, d^{2} x^{5} + c d x^{4} + \frac{4}{3} \, c^{2} x^{3} + 4 \, a c x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]