# Integrate sinx*cox* using double angle

1. Aug 5, 2013

### Jude075

1. The problem statement, all variables and given/known data

∫ Sinx cos x dx

2. Relevant equations

3. The attempt at a solution
If you integrate it using substitution, you get -cos2(x)/2but if you use double angle formula to rewrite the problem, it will be ∫1/2 sin(2x), and integrate it, you get -cos(2x)/4. isn't it weird?

2. Aug 5, 2013

### voko

You are forgetting that each of those two integrals must have $+ C$ appended to it. Now recall that $\cos 2x = 2 \cos^2 x - 1$.

3. Aug 5, 2013

### D H

Staff Emeritus
What voko said is exactly right. To elaborate, these two apparently different integrals differ only by a constant.

4. Aug 5, 2013

### Jude075

So if I was to find the indefinite integral, both answers were right?

5. Aug 5, 2013

### voko

None is correct unless you add the indefinite constant.