ज्ञात करें `int (dx)/(3+2sin x+ cosx)`

Explanation

माना की `I = int (dx)/(3+2 sin x + cos x)`
`tan ""x/2 =t` रखे, तो `1/2 sec^2 ""x/2 dx = dt" ":." "dx = (2dt)/(1+t^2)`
अब, `I=int (2dt//(1+t^2))/(3+2(2t)/(1+t^2)+(1-t^2)/(1+t^2))=int (2dt)/(3(1+t^2)+4t+1-t^2)=int (dt)/(t^2+2t+2)`
`=int (dt)/((t+1)^2+2)=tan^(-1)(t+1)+c = tan^(-1)+c=tan^(-1)(1+tan""x/2)+c`