Question

How do you integrate `int sin2x dx`?

Answer 1

`intsin(2x)dx=-1/2cos(2x)+C`

Explanation:

Using integration by substitution together with the known integral `intsin(x)dx = -cos(x)+C`, we first let `u = 2x => du = 2dx`. Then

`intsin(2x)dx = 1/2intsin(2x)2dx`

`=1/2intsin(u)du`

`=1/2(-cos(u))+C`

`=-1/2cos(2x)+C`