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Find the following integrals: ∫sec2xcosec2xdx

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Question

Find the following integrals:

`int(sec^2x)/(cosec^2x) dx`

Sum
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Solution

Let `I = int (sec^2 x)/(cosec^2)  dx`

`I = int (1/(cos^2 x))/(1/(sin^2 x))  dx`

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

`I = int tan^2 x  dx`

`I = int sec^2 x - 1  dx`

`I = int sec^2 x  dx - int 1  dx`

I = tan x - x + C

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Chapter 7: Integrals - Exercise 7.1 [Page 299]

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NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 7 Integrals
Exercise 7.1 | Q 19 | Page 299

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