Integrate sin^2x

To integrate sin^2x, also written as ∫sin²x dx, sin squared x, and (sin x)^2, we start by using standard trig identities to simplify the integral.

We start by using the standard trig identity sin²x+cos²x=1 and rearrange it for sin²x. This is basic and straightforward.

We then recall another standard trig identity for double angle where cos2x=cos²x-sin²x, and rearrange it for cos²x.

We substitute the second trig identity into the first and rearrange for sin²x.

As you can see, we now have an equivalent integral that is the same as the original, but easier to perform. Although the ½ fraction is easy to integrate, we need to focus on integrating the cos2x term, which we achieve using the u substitution method.

Using the u substitution, we integrate cos2x dx to give part of the answer.

We substitute the result we gained from integrating cos2x, and then simplify to give the final answer.