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Question
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
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Solution
Let I = `int (3"x"^3 - 2sqrt"x")/"x"` dx
`= int ("3x"^3/"x" - "2x"^(1/2)/"x")` dx
`= int (3"x"^2 - 2"x"^(-1/2))` dx
`= 3 int "x"^2 * "dx" - 2 int "x"^(-1/2) * "dx"`
`= 3 ("x"^3/3) - 2("x"^(1/2)/(1/2))` + c
∴ I = x3 - 4`sqrt"x"` + c
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