Evaluate: ∫x2+2x+5 dx - Mathematics and Statistics

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Sum

Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx

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Solution

Let I = `int sqrt("x"^2 + 2"x" + 5)` dx

`= int sqrt("x"^2 + 2"x" + 1 + 4)` dx

`= int sqrt(("x + 1")^2 + (2)^2)` dx

`= ("x" + 1)/2 sqrt(("x" + 1)^2 + (2)^2) + (2)^2/2 log |("x + 1") + sqrt(("x + 1")^2 + (2)^2)|` + c

∴ I = `("x" + 1)/2 sqrt("x"^2 + 2"x" + 5) + 2 log |("x + 1") + sqrt("x"^2 + 2"x" + 5)|` + 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) vi) | Page 139

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