Optimal. Leaf size=36 \[ \frac{x^8}{8}-\frac{8 x^7}{7}+\frac{11 x^6}{3}-\frac{24 x^5}{5}+\frac{9 x^4}{4} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0125975, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, Rules used = {698} \[ \frac{x^8}{8}-\frac{8 x^7}{7}+\frac{11 x^6}{3}-\frac{24 x^5}{5}+\frac{9 x^4}{4} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 698
Rubi steps
\begin{align*} \int x^3 \left (3-4 x+x^2\right )^2 \, dx &=\int \left (9 x^3-24 x^4+22 x^5-8 x^6+x^7\right ) \, dx\\ &=\frac{9 x^4}{4}-\frac{24 x^5}{5}+\frac{11 x^6}{3}-\frac{8 x^7}{7}+\frac{x^8}{8}\\ \end{align*}
Mathematica [A] time = 0.0006064, size = 36, normalized size = 1. \[ \frac{x^8}{8}-\frac{8 x^7}{7}+\frac{11 x^6}{3}-\frac{24 x^5}{5}+\frac{9 x^4}{4} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.039, size = 27, normalized size = 0.8 \begin{align*}{\frac{9\,{x}^{4}}{4}}-{\frac{24\,{x}^{5}}{5}}+{\frac{11\,{x}^{6}}{3}}-{\frac{8\,{x}^{7}}{7}}+{\frac{{x}^{8}}{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.99327, size = 35, normalized size = 0.97 \begin{align*} \frac{1}{8} \, x^{8} - \frac{8}{7} \, x^{7} + \frac{11}{3} \, x^{6} - \frac{24}{5} \, x^{5} + \frac{9}{4} \, x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.48796, size = 69, normalized size = 1.92 \begin{align*} \frac{1}{8} x^{8} - \frac{8}{7} x^{7} + \frac{11}{3} x^{6} - \frac{24}{5} x^{5} + \frac{9}{4} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.059099, size = 31, normalized size = 0.86 \begin{align*} \frac{x^{8}}{8} - \frac{8 x^{7}}{7} + \frac{11 x^{6}}{3} - \frac{24 x^{5}}{5} + \frac{9 x^{4}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.12255, size = 35, normalized size = 0.97 \begin{align*} \frac{1}{8} \, x^{8} - \frac{8}{7} \, x^{7} + \frac{11}{3} \, x^{6} - \frac{24}{5} \, x^{5} + \frac{9}{4} \, x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]