How do you solve integrals which are the result of a chain rule e.g. the integral of sin(2x+1)

∫sin(2x + 1)dx[newline]In this case the easiest way to solve the integral is to perform a substitution. The substitution should reduce the integral to something you can solve. In this case we will[newline]let u = 2x + 1[newline]This allows the integral to be written as[newline]∫sin(u)dx[newline]We are not done yet as there is still the dx to deal with. The next step is to differentiate u[newline]du/dx = 2[newline]We can then rearrange this equation to get a substitution for dx[newline]dx = du/2[newline]Subbing this into the integral gives[newline]1/2 ∫sin(u)du[newline]Which can be solved using the standard integral on the formula sheet to give[newline]-1/2 cos(u) + C[newline]All that is left to do now is replace u with 2x + 1 giving the answer[newline]∫sin(2x + 1) = -1/2 cos(2x + 1) + C