Evaluate the following. ∫1x2+4x-5 dx - Mathematics and Statistics

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Sum

Evaluate the following.

`int 1/("x"^2 + 4"x" - 5)` dx

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Solution

Let I = `int 1/("x"^2 + 4"x" - 5)` dx

`= int 1/("x"^2 + 4"x" + 4 - 4 - 5)` dx

`= int 1/(("x + 2")^2 - 9)  "dx"`

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

`= 1/(2 xx 3)  log  |(("x" + 2) - 3)/(("x" + 2) + 3)|` + c

∴ I = `1/6  log  |("x" - 1)/("x" + 5)|` + c

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Chapter 5: Integration - EXERCISE 5.4 [Page 129]

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