Evaluate: (i) `int(e^x)/(sqrt(5-4\ e^x-e^(2x)))\ dx` (ii) `int(cosx)/(sqrt(sin^2x-2sinx-3))\ dx`

Explanation

(i)I= `int(e^x)/(sqrt(5-4\ e^x-e^(2x)))\ dx`

let `e^x=t`


`e^xdx=dt`

`I= int(1)/(sqrt(5-4t-t^2))dx`

`I=int(1)/(sqrt(t^2-4t+4+1))dx`

`I=int(1)/(sqrt((t-2)^2+1))dx`

`I=ln∣​(t−2)+sqrt((t−2)^2+1
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