Recall chain rule: 

u = 2x +1; du = 2dx → dx = \(\frac{du}{2}\)
u\(^3\) = ∫ u\(^3\) \(\frac{du}{2}\) → \(\frac{1}{2}\) ∫ u\(^3\)

= \(\frac{1*u^4}{2*4}\) 

= \(\frac{u^4}{8}\) → \(\frac{{2x+1}^4}{8}\) + C