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Evaluate : (i) int (cos2x+2sin^2x)/(sin^...

Evaluate : (i) `int (cos2x+2sin^2x)/(sin^2x)dx` (ii) `int(2cos^2x-cos2x)/(cos^2x)dx`

Text Solution

Verified by Experts

(i) Let `I = int (cos2x+2sin^2x)/sin^2x dx`
`=>I = int ((2cos^2x-1)+2sin^2x)/sin^2x dx`
`=>I = int ((2(cos^2x+sin^2x)-1)/sin^2x dx`
`=>I = int (2-1)/sin^2x dx`
`=>I = int 1/sin^2x dx`
`=>I = int cosec^2xdx`
`=>I = -cotx+c`

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