# Integral of sin(2x)dx

1. Apr 4, 2010

### physx_420

1. The problem statement, all variables and given/known data
$$\int$$ sin(2x)dx

2. Relevant equations
I know the integral of sin(x)dx = -cos(x) + C

3. The attempt at a solution
What I did was to say that the integral is -cos(2x) +C, which isn't the correct answer...I should have gotten -1/2(cos(2x)) +C. I can see that this is the correct answer when I differentiate it via chain rule and get sin(2x), however I can't seem to integrate the problem to get the right answer. Can someone walk me through it please.....

2. Apr 4, 2010

### Staff: Mentor

Use substitution, with u = 2x, du = 2dx. Integration by substitution is the reverse of the chain rule in differentiation.

3. Apr 4, 2010

### physx_420

ah so that's where I went wrong....I tried u substitution but I used u=sin2x instead of u=2x. thanks mark44.