Question

indefinite integrals (3x+2)^2 dx

Answer 1

How would you find the definite integral of x^2 with respect to x?
Integrating (3x+2)^2 with respect to x involves just a little more work: substitution.
Familiar with that? Substitution results in a simpler-looking integral that is indeed simpler to integrate.
Try letting u = 3x+2. ("u" represents your substitution for 3x+2.)
Find (du/dx) (write an actual equation, du/dx = ?)
Solve the resulting equation for dx.
In the original integral, substitute u for 3x+2, and substitute du/3 for dx.
Integrate.
Finally, re-substitute: replace u in the integral with 3x+2. That's it.