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Question
Integrate the following with respect to x.
`sqrt(4x^2 - 5)`
Solution
`int sqrt(4x^2 - 5) "d"x = int sqrt((2x)^2 - (sqrt(5))^2) "d"x`
Let 2x = t
Then 2dx = dt
= `1/2 int sqrt("t"^2 - (sqrt(5))^2) "dt"`
= `1/2 ["t"/2 sqrt("t"^2 - 5) - 5/2 log|"t" + sqrt("t"^2 - 5)|] + "c"`
= `1/4 [2x sqrt(4x^2 - 5) - 5 log|2x +sqrt(4x^2 - 5)| + "c"`
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