Integrating sin(2x)dx: Solving for the Integral of a Trigonometric Function

[physx_420]

Homework Statement

\int sin(2x)dx

Homework Equations

I know the integral of sin(x)dx = -cos(x) + C

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...

 

[Mark44]

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

 

[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.