Hello, free_to_fly!

Use the subsitution to find:

I used: .

and that: .

So the integral becomes: .

and using the doule angle formula, I get: .

Giving: .

but then I can go no further because the answer had in it

and I don't know where that came from.

Evaluate and we get: .

. . and one of the basic identities is: .

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Where did that identity come from?

. . You can derive it yourself.

We have: .

Then: .

From the definition: .

Multiply by

We have: . . . . a quadratic in

Quadratic Formula: .

Since must be positive, we have: .

Hence: .

Therefore: . . . . ta-DAA!

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Similarly, you can derive other identities:

. .

. .

. .

Have I memorized these formulas? . . .certainly not!

I have them on my handy-dandy Formula Sheets.

[I need my brain cells to remember my name.]