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Evaluate ∫3x3-2xx dx - Mathematics and Statistics

Sum

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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