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Question
Evaluate: `int 1/(sqrt("x") + "x")` dx
Solution
Let I = `int 1/(sqrt("x") + "x")` dx
`= int 1/(sqrt"x" (1 + sqrt"x"))` dx
Put `1 + sqrt"x"` = t
∴ `1/(2sqrt"x") "dx"` = dt
∴ `1/sqrt"x" "dx"` = 2 dt
∴ I = `int (2 * "dt")/"t"`
`= 2 int 1/"t"` dt
= 2 log |t| + c
∴ I = 2 log `|1 + sqrt"x"|` + c
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