Question

integration (sin2x)dx​

Answer 1

Integrate sin2x

∫sin2x dx

To integrate sin2x, also written as ∫sin2x dx, and sin 2x, we usually use a u substitution to build a new integration in terms of u.

u=2x

Let u=2x.

du/dx

Then du/dx = 2

dx

We rearrange to get an expression for dx in terms of u.

New integration in terms of u.

As you can see, we now have a new integration in terms of u, which means the same thing. We get this by replacing 2x with u, and replacing dx with ½ du.

moving ½ outside of the integral sign.

We move the ½ outside of the integral as it is simply a multiplier.

integral of sinu

We now have a simple integration with sinu that we can solve easily.

Reintroduce ½ constant.

We remember the ½ outside the integral sign and reintroduce it here.

-½cos2x + C