Maharashtra State BoardHSC Commerce 12th Board Exam
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Choose the correct alternative from the following. ∫(x+1x)3dx = - Mathematics and Statistics

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MCQ

Choose the correct alternative from the following.

`int ("x" + 1/"x")^3 "dx"` = 

Options

  • `1/4 ("x" + 1/"x")^4` + c

  • `"x"^4/4 + "3x"^2/2 + 3 log "x" - 1/"2x"^2 + "c"`

  • `"x"^4/4 + "3x"^2/2 + 3 log "x" + 1/"x"^2 + "c"`

  • `("x" - "x"^-1)^3` + c

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Solution

`"x"^4/4 + "3x"^2/2 + 3 log "x" - 1/"2x"^2 + "c"`

Explanation:

Let I = `int ("x" + 1/"x")^3 "dx"` 

`int ("x"^3 + "3x" + 3/"x" + 1/"x"^3)` dx

`= "x"^4/4 + 3 "x"^2/2 + 3 log |"x"| - 1/"2x"^2` + 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 1.07 | Page 137
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