Evaluate: (i) `int(e^(x-1)+x^(e-1))/(e^x+x^e)\ dx` (ii) `int1/(sinxcos^2x)\ dx`

Explanation

(i)

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

`Putting e^{x}+x^{e}=t `

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

`Rightarrow e(e^{x-1}+x^{e-1})=frac{d t}{d x} `

`Rightarrow(e^{x-1}+x^{e-1}) d x=frac{d t}{e} `

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

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