State whether the following statement is True or False. For ∫x - 1(x + 1)3 exdx=ex f(x) + c, f(x) = (x + 1)2. - Mathematics and Statistics

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MCQ
True or False

State whether the following statement is True or False.

For `int ("x - 1")/("x + 1")^3  "e"^"x" "dx" = "e"^"x"` f(x) + c, f(x) = (x + 1)2.

Options

  • True

  • False

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Solution

False

Explanation:

Let I =`(("x - 1"))/(("x + 1")^3) * "e"^"x"` dx

`= int "e"^"x" [(("x + 1") - 2)/("x + 1")^3]` dx

`= int "e"^"x" [1/("x + 1")^2 - 2/("x + 1")^3]` dx

`= int "e"^"x" [("x + 1")^-2 - 2("x + 1")^-3]` dx

Put f(x) = (x + 1)-2

∴ f '(x) = - 2 (x + 1)-3

∴ I = `"e"^"x" ["f"("x") + "f" '("x")]` dx

`= "e"^"x" * "f"("x")` + c

`= "e"^"x" * ("x + 1")^-2` + c

∴ f(x) = (x + 1)-2 

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Chapter 5: Integration - MISCELLANEOUS EXERCISE - 5 [Page 138]

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Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 5 Integration
MISCELLANEOUS EXERCISE - 5 | Q III. 5. | Page 138

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