OK I'm studying for a calculus exam and I ran across a problem where I thought I did everything right, but I can't know for sure because it's an even problem and I don't have an answer.

Problem:

What I did:

Splitting into squares:

Using cos^2 + sin^2 = 1:

Substituting:

Foiling:

Integrating:

Unsubstituting:

Answer:

I typed the problem into Wolfram Alpha and it gave me this:

This looks alot different than my answer, and they did it using something called a 'reduction formula', which seems like something I would never remember. Is my answer wrong, or did they just do it differently? Or is Wolfram Alpha not the best place to be checking my answers?

ThanksYou did not make any mistake.

Since: .