Evaluate the following integrals: i. ∫ (1 + tan x)/(x + log sec x) dx

Question

Evaluate the following integrals:

i. \(\int \frac{(1 + tan\,x)}{(x + log\,sec\,x)}dx\) ∫ (1 + tan x)/(x + log sec x) dx

ii. \(\int \frac{(1 - sin\,2x)}{(x + cos^2 x)}dx\)

Answer 1

(i)

Therefore,

Put x + log (sec x) = t

(ii)

Therefore,