∫1sinx.cos2xdx = ______. - Mathematics

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MCQ
Fill in the Blanks

`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

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Solution

`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

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