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int((2+secx)secx)/((1+2secx)^2)dx=...

`int((2+secx)secx)/((1+2secx)^2)dx=`

A

`(1)/("2 cosec x"+cotx)+C`

B

`"2 cosec x"+cotx+C`

C

`(1)/("2 cosec x"-cotx)+C`

D

`"2 cosec x"-cotx+C`

Text Solution

Verified by Experts

The correct Answer is:
A
`I=int((2cosx+1))/((2+cosx)^(2))dx`
`=int((2+cosx)cosx+sin^(2)x)/((2+cosx)^(2))dx`
`=int(cosx)/(2+cosx)dx-int(-sin^(2)x)/((2+cosx)^(2))dx`
`=(sinx)/(2+cosx)+C`
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