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Question
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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