Evaluate: (i) `intcot^3x\ cos e c^2x\ dx` (ii) `int({e^msin^(-1)x})/(sqrt(1-x^2))\ dx`

Explanation

`(i)`Let
`t=cotx`
`=>dt=−cosec^2 xdx`
Given,
`I=intcot^3x\ cos e c^2x\ dx`
`=-int t^3dt`
`=-1/4t^4+c`
`=-1/4cot^4x+c`


`(ii)`Given,
`int({e^msin^(-1)x})/(sqrt(1-x^2))\ dx`
let`t=sin^(-1)x`
`dt=1/sqrt(1-x^2)dx`
`int(e^m sin^(-1)x)/sqrt(1-x^2)dx=inte^(mt)dt`
`=1/me^(mt)+c`
`=1/me^(msin^(-1)x)+C`.