Re: Trigonometric Integral

Hey infraRed.

One that comes to mind hint-wise is to multiply the inside by (1+sin(t))/(1+sin(t)) which will make the denominator 1 - sin^2(t) = cos^2(t) and this will simplify to sec^2(t) - tan^2(t) which is integrable using standard results.

Re: Trigonometric Integral

Hello, infraRed!

Multiply by

. . . . . . . . . . .

And you can integrate: .

Right?

Re: Trigonometric Integral

It might be easier for the OP to write as there is a more obvious substitution.

Re: Trigonometric Integral

Thanks all! Forgot about the multiply-by-1 technique.

Re: Trigonometric Integral

An alternative method for dealing with integrals involving trig functions like this is to use the half-angle substitution

That gets you and

For this particular example it's not as neat as the routine already demonstrated, but there are times when it's the thing to do.

Re: Trigonometric Integral

Hint. Final answer should come to 2sin(t/2)/(cos(t/2)-sin(t/2)) + C

Re: Trigonometric Integral

Hint. Final answer should come to 2sin(t/2)/(cos(t/2)-sin(t/2)) + C