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Question
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
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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