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Choose the correct alternative from the following. ∫(e2x+e-2xex)dx = - Mathematics and Statistics

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MCQ

Choose the correct alternative from the following.

`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` = 

Options

  • `"e"^"x" - 1/(3"e"^"3x")` + c

  • `"e"^"x" + 1/(3"e"^"3x")` + c

  • `"e"^"-x" + 1/(3"e"^"3x")` + c

  • `"e"^"-x" + 1/(3"e"^"3x") + "c"`

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Solution

`"e"^"x" - 1/(3"e"^"3x")` + c

Explanation:

`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx" = int ("e"^"x" + "e"^(-3"x"))` dx

`= "e"^"x" - 1/3 "e"^(-3"x") + "c"`

Concept: Methods of Integration: Integration by Parts
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 5 Integration
Miscellaneous Exercise 5 | Q 1.08 | Page 137
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