Evaluate: (i) `int(cos2x+x+1)/(x^2+sin2x+2x)\ dx` (ii) `int1/(cos(x+a)cos(x+b))\ dx`

Explanation

(i)

`Let {I}=int frac{cos 2 x+x+1}{x^{2}+sin 2 x+2 x} d x`

Putting `x^{2}+sin 2 x+2 x=t`


`Rightarrow 2 x+2 cos 2 x+2=frac{d t}{d x} `

`Rightarrow(x+cos 2 x+1) d x=frac{d t}{2} `

`therefore I=frac{1}{2} int frac{1}{t} d t `

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