Question

calcule a integral x^2(1+x)^2 dx

Answer 1

Boa noite.

$\displaystyle \int x^2(1+x)^2 \, dx \\ \\ \\ \int x^2 \cdot (1+x) \cdot (1+x) \, dx \\ \\ \\ \int x^2 \cdot (x^2+2x+1) \, dx \\ \\ \\ \int x^4+2x^3+x^2 \, dx \\ \\ \\ \boxed{\boxed{\frac{1}{5}x^5+\frac{1}{2}x^4+\frac{1}{3}x^3+c}}$

Answer 2

Olá, boa noite ☺

Resolução:

$\int (x^2\cdot(1+x)^2) dx \\ \\ \int (x^2\dot(x^2+2x +1)) dx \\ \\ \int (x^4+2x^3+x^2) dx \\ \\\boxed{= \dfrac{x^5}{5} + \dfrac{x^4}{4} + \dfrac{x^3}{3} +c }$

Bons estudos =)