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Question
Integrate the following functions with respect to x:
`sqrt((x + 1)^2 - 4)`
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Solution
`int sqrt((x + 1)^2 - 4) "d"x = int sqrt((x + 1)^2 - 2^2) "d"x`
Put x + 1 = t
dx = dt
= `int sqrt("t"^2 - 2^2) "dt"`
= `"t"/2 sqrt("t"^2 - 2^2) - 2^2/2 log |"t" + sqrt("t" - 2^2)| + "c"`
= `((x + 1))/2 sqrt((x + 1)^2 - 2^2) - 2 log|(x + 1) + sqrt((x + 1)^2 - 2^2)| + "c"`
`int sqrt((x + 1)^2 - 4) "d"x = ((x + 1))/2 sqrt((x + 1)^2 - 4) - 2 log |(x + 1) + sqrt((x + 1)^2 - 4)| + "c"`
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