Integrate sinx*cox* using double angle

[Jude075]

Homework Statement

∫ Sinx cos x dx

Homework Equations

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?

 

[voko]

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

 

[D H]

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?

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

 

[Jude075]

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

 

[voko]

None is correct unless you add the indefinite constant.