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Question
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Solution
Let I = `int "dx"/sqrt(4"x"^2 - 5)`
`= int 1/(sqrt (4("x"^2 - 5/4)))`dx
`= 1/2 int 1/(sqrt("x"^2 - ((sqrt5)/2)^2))` dx
`= 1/2 log |"x" + sqrt("x"^2 - (sqrt5/2)^2)|` + c
∴ I = `1/2 log |"x" + sqrt("x"^2 - 5/4)|` + c
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