Maharashtra State BoardHSC Commerce 12th Board Exam
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Choose the correct alternative from the following. ∫(x3+3x2+3x+1)(x + 1)5 dx = - Mathematics and Statistics

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MCQ

Choose the correct alternative from the following.

`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5  "dx"` = 

Options

  • `(-1)/"x + 1"` + c

  • `((-1)/"x + 1")^5` + c

  • log(x + 1) + c

  • log |x + 1|5 + c 

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Solution

`(-1)/"x + 1"` + c

Explanation:

`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5  "dx" = int ("x + 1")^3/("x + 1")^5` dx

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

`= (-1)/"x + 1"` + 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 1.1 | Page 138
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