ज्ञात करें ` int (sin x)/((2 + cos x )( 5 + cos x))dx`

Explanation

माना की `I = int (sin x)/((sin+cosx)(5+cos x))dx`
`cos x = z` रखे तो `sin x dx = -dz`
अब, `I = int (-dz)/((2+z)(5+z))=1/3 int[1/(5+z)-1/(2+z)]dz` [ partial fractions से ]
`=1/3 [log | 5+z|-log| 2+z|] +c =1/3 log |(5+z)/(2+z)|+c`
`=1/3|(5+cosx)/(2+cosx)|+c=1/3log((5+cosx)/(2+cosx))+c`