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Evaluate the following. ∫17+6x-x2 dx - Mathematics and Statistics

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Question

Evaluate the following.

`int 1/(7 + 6"x" - "x"^2)` dx

Sum
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Solution

Let I = `int 1/(7 + 6"x" - "x"^2)` dx

`= int 1/(7 + 9 - 9 + 6"x" - "x"^2)` dx

`= int 1/(16 - ("x"^2 - 6"x" + 9))` dx

`= int 1/((4)^2 - ("x" - 3)^2)` dx

`= 1/(2xx4) log |(4 + "x" - 3)/(4 - ("x" - 3))|` + c

∴ I = `1/8 log |(1 + "x")/(7 - "x")|` + c

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Chapter 5: Integration - EXERCISE 5.4 [Page 129]

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