Question

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

Options

• secx + log | secx + tanx | + c

• secx . tanx + c

• secx + log | secx – tanx | + c

• secx + log | cosecx – cotx | + c

Answer 1

`int 1/(sinx.cos^2x)dx` = secx + log | cosecx – cotx | + c.

Explanation:

`int dx/(sinx cos^2x) = int (sin^2x + cos^2x)/(sinx cos^2x) dx`

= `int sinx/(cos^2dx)dx + int (dx)/sinx`

= `int tan x sec x + int "cosec"  x  dx`

= sec x + log|cosec x – cot x| + c