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Question
Integrate the following functions with respect to x :
`(x^3 + 4x^2 - 3x + 2)/x^2`
Solution
`(x^3 + 4x^2 - 3x + 2)/x^2 "d"x = int (x^3/x^2 + (4x^2)/x^2 - (3x)/x^2 + 2/x^2) d"x`
= `int (x + 4 - 3/x + 2/x^2) "d"x`
= `int x"d"x + int4"d"x - int 3/x "d"x + int 2/x^2 "d"x`
= `int x"d"x + 4int "d"x - 3int ("d"x)/x + 2int ("d"x)/x^2`
= `x^2/2 + 4x - 3log|x| + 2intx^-2 "d"x`
= `x^2/2 + 4x - 3log|x| + 2 * (x^(-2 + 1))/(- 2 + 1) + "c"`
= `x^2/2 + 4x - 3 log|x| + 2 xx (x^-1)/(-1) + "c"`
= `x^2/2 + 4x - 3log|x| - 2/x + "c"`
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