`int (sin 2 x dx)/(a cos^(2) x + b sin^(2)x)` का मान ज्ञात कीजिये ।

Explanation

माना `I = int (sin 2x dx)/(a cos^(2) x + b sin^(2)x)`
माना `" "a cos^(2) x + b sin^(2) x = t`
`rArr " "(-2a sin x cos x + 2b sin x cos x) dx = dt`
`rArr " "(b-a) sin 2x dx = dt`
`rArr" "sin2x dx = (dt)/(b-a)`
`therefore" "I = ((1)/(b-a))int(dt)/(t) = (1)/(b-a) log t`
`=(1)/(b-a)log[a cos^(2) x + bsin^(2) x]`