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Question
Evaluate the following.
`int 1/(4"x"^2 - 20"x" + 17)` dx
Solution
Let I = `int 1/(4"x"^2 - 20"x" + 17)` dx
= `1/4 int 1/("x"^2 - 5"x" + 17/4)` dx
= `1/4 int 1/("x"^2 - 2 * 5/2 "x" + 25/4 - 25/4 + 17/4)` dx
= `1/4 int 1/(("x" - 5/2)^2 - 8/4)` dx
= `1/4 int 1/(("x" - 5/2)^2 - (sqrt2)^2)` dx
= `1/4 xx 1/(2sqrt2) log |("x" - 5/2 - sqrt2)/("x" - 5/2 + sqrt2)|` + c
∴ I = `1/(8sqrt2) log |(2"x" - 5 - 2sqrt2)/(2"x" - 5 + 2sqrt2)|` + c
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