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Question
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
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Solution
`int (1)/(4x^2 - 20x + 17).dx`
= `(1)/(4) int (1)/(x^2 - 5x + 17/4).dx`
= `(1)/(4) int (1)/((x^2 - 5x + 25/4) - (25)/(4) + (17)/(4)).dx`
= `(1)/(4) int (1)/((x - 5/2)^2 - (sqrt(2))^2).dx`
= `(1)/(4) xx (1)/(2sqrt(2))log|(x - 5/2 - sqrt(2))/(x - 5/2 + sqrt(2))| + c`
= `(1)/(8sqrt(2))log |(2x - 5 - 2sqrt(2))/(2x - 5 + 2sqrt(2))| + c`.
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