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int(1)/(sinx*cos^(2)x)dx=...

`int(1)/(sinx*cos^(2)x)dx=`

A

`secx+log|secx+tanx|+C`

B

`secx+log|secx+tanx|+C`

C

`secx+log|secx-tanx|+C`

D

`secx+log|"cosec"x-cotx|+C`

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`l=int(dx)/(sinx*cos^(2)x)`
`rArr" "l=int(sin^(2)x+cos^(2)x)/(sinxcos^(2)x)dx`
`rArrl=int(sin^(2)x)/(sinxcos^(2)x)dx+int(cos^(2)x)/(sinxcos^(2)x)dx`
`rArrl=intsecxtanxdx+int"cosec"xdx`
`rArrl=secx+log|"cosec"x-cotx|+C`
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