Evaluate: ∫ex1+x/(2+x)2 dx - Mathematics and Statistics

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Sum

Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx

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Solution

Let I = `int "e"^"x" (1 + "x")/(2 + "x")^2` dx

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

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

Let f(x) = `1/(2 + "x")`

∴ f '(x) = `(-1)/(2 +"x")^2`

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

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

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

∴ I = `"e"^"x"/(2 + "x")` + c

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Chapter 5: Integration - MISCELLANEOUS EXERCISE - 5 [Page 139]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 5 Integration
MISCELLANEOUS EXERCISE - 5 | Q IV. 4) ii) | Page 139

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