ज्ञात करें `int (sin 2x)/((1+sin x)( 2+sinx)) dx`

Explanation

माना की `I =int (sin 2x)/((1+sin x)( 2+sinx)) dx`
`=int ("2 sin x cos x")/((1+sin x)(2+sin x))dx" ...(1)"`
sin x = t रखे, तो cos x dx = dt
(1) से, `I = int (2t)/((1+t)(2+t))dt = int [(-2)/(t+1)+ 4/(t+2)] dt +c ` [ partial fraction से ]
`=-2log | t+1 | +4 log | t + 2| +c`
` = -2log | 1+sin x|+4 log | 2+sin x|+c`
`= -2log (1+sin x)+4log (2+sinx)+c`