Evaluate the following : ∫sec3x.dx - Mathematics and Statistics

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Sum

Evaluate the following:

`int sec^3x.dx`

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Solution

Let I = `int sec^3x.dx`

= `int sec x sec^2x.dx`

= `sec x int sec^2x.dx - int[d/dx(secx) int sec^2x.dx].dx`

= `secx tanx- int (secx tanx)(tanx).dx`

= `secx tanx - int secx tan^2x.dx`

= `secx tanx - int secx (sec^2x - 1).dx`

= `secx tanx - int sec^3x.dx + int secx.dx`

∴ I = sec x tan x – I + log |sec x + tanx|

∴ 2I = sec x tan x + log |sec x  + tan x|

∴ I = `(1)/(2)[secx tanx + log |secx + tan|] + c`.

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Chapter 3: Indefinite Integration - Exercise 3.3 [Page 137]

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