Evaluate `int(dx)/((2+cosx))`.

1.	Evaluate `int(dx)/((2+cosx))`.
Answer» We have `int(dx)/((2+cosx))=int(dx)/(1+(1+cosx))=int(dx)/(1+2cos^(2)(x//2))=int(sec^(2)(x//2)dx)/(sec^(2)(x//2)+2)` [ dividing the num . And denom . By `cos^(2)(x//2)`] `=int(sec^(2)(x//2))/(3+tan^(2)(x//2))dx=2int(dt)/(3+t^(2))`, where tan `(x//2)=` `=2int(dt)/((sqrt(3))^(2)+t^(2))=2(1)/(sqrt(3))"tan"^(-1)(t)/(sqrt(3))+C` `=(2)/(sqrt(3))tan^(-1)[(tan(x//2))/(sqrt(3))]+C`.

Discussion

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