Integrate the following functions w.r.t. x : [2 + cot x – cosec2x]ex - Mathematics and Statistics

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Sum

Integrate the following functions w.r.t. x : [2 + cot x – cosec2x]e 

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Solution

Let I = `int e^x [2 + cotx - "cosec"^2x].dx`

Put f(x) = 2 + cot x

∴ f'(x) = `d/dx (2 + cot x)`

= `d/dx (2) + d/dx (cot x)`

= 0 – cosec2x
= – cosec2x
∴ I = `int e^x [f(x) + f'(x)].dx`
= ex f(x) + c
= ex (2 + cot x) + c.

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Chapter 3: Indefinite Integration - Exercise 3.3 [Page 138]

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