Evaluate the following integrals: ∫ dx/(a cos x + b sin x)^2, a > 0 and b > 0

Question

Evaluate the following integrals:

\(\int \frac{dx}{(a\,cos\,x + b\,sin\,x)^2},\) a > 0 and b > 0

∫ dx/(a cos x + b sin x)², a > 0 and b > 0

Answer 1

\(\int \frac{dx}{(a\,cos\,x + b\,sin\,x)^2}\)

∫ dx/(a cos x + b sin x)², a > 0 and b > 0

Taking b cos x common from the denominator we get,

Resubstituting the value of t = (a/b) + tan x we get