Optimal. Leaf size=22 \[ \frac{4 x^7}{7}+\frac{2 x^6}{3}+\frac{x^5}{5} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0103443, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {647, 43} \[ \frac{4 x^7}{7}+\frac{2 x^6}{3}+\frac{x^5}{5} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 647
Rule 43
Rubi steps
\begin{align*} \int x^2 \left (x+2 x^2\right )^2 \, dx &=\int x^4 (1+2 x)^2 \, dx\\ &=\int \left (x^4+4 x^5+4 x^6\right ) \, dx\\ &=\frac{x^5}{5}+\frac{2 x^6}{3}+\frac{4 x^7}{7}\\ \end{align*}
Mathematica [A] time = 0.0012019, size = 22, normalized size = 1. \[ \frac{4 x^7}{7}+\frac{2 x^6}{3}+\frac{x^5}{5} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0., size = 17, normalized size = 0.8 \begin{align*}{\frac{{x}^{5}}{5}}+{\frac{2\,{x}^{6}}{3}}+{\frac{4\,{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.950201, size = 22, normalized size = 1. \begin{align*} \frac{4}{7} \, x^{7} + \frac{2}{3} \, x^{6} + \frac{1}{5} \, x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.60464, size = 39, normalized size = 1.77 \begin{align*} \frac{4}{7} x^{7} + \frac{2}{3} x^{6} + \frac{1}{5} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.053199, size = 17, normalized size = 0.77 \begin{align*} \frac{4 x^{7}}{7} + \frac{2 x^{6}}{3} + \frac{x^{5}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.10123, size = 22, normalized size = 1. \begin{align*} \frac{4}{7} \, x^{7} + \frac{2}{3} \, x^{6} + \frac{1}{5} \, x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]