Evaluate the following integrals:
We know cos2x + sin2x = 1, 2sinxcosx = sin2x
∴ Denominator can be written as
cos2x + sin2x + 2sinxcosx = (sinx + cosx)2
∴ Now the given equation becomes
⇒
Assume cosx + sinx = t
∴ d(cosx + sinx) = dt
= cosx - sinx
∴ dt = cosx – sinx
⇒
⇒
⇒
⇒
But t = cosx + sinx
⇒