Question

Evaluate the integral: \[ \int (x+2)^2 \, dx = ? \]

Hint:

When integrating polynomials or binomials raised to powers, first expand the expression to simplify integration.

Answer 1

First, expand the integrand: \[ (x+2)^2 = x^2 + 4x + 4 \] Now integrate term by term: \[ \int (x^2 + 4x + 4) \, dx = \int x^2 \, dx + \int 4x \, dx + \int 4 \, dx \] \[ = \frac{x^3}{3} + 2x^2 + 4x + c \]