Antiderivatives

Question

Here are two antiderivative formulas.

∫ = integral symbol

I. ∫ 2 sin x cos x = dx = -cos^2 x + C

II. ∫ 2 sin x cos dx = sin^2x + C

Which of the antiderivative formulas, if any, are true?

I only

II only

both I and II

neither I nor II

Answer 1

You can use u-substitution to figure out the antiderivative. Let u = sinx, then du = cosxdx. So this integral simplifies to:

∫ 2udu

Can you figure it out from here?