Evaluate: (i) `int1/(e^x+1)\ dx` (ii) `int(cotx)/(logsinx)\ dx`

Explanation

(i)

`text { Let } {I}=int frac{1}{e^{x}+1} d x `

`=int frac{e^{-x}}{1+e^{-x}} d x `

`text { Putting } e^{-x}=t `

`Rightarrow-e^{-x}=frac{d t}{d x} `

`Rightarrow e^{-x} d x=-d t `

`therefore I=int frac{-1}{1+t} d t `

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