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Question
Integrate the following with respect to x.
`sqrt(x)(x^3 - 2x + 3)`
Solution
`sqrt(x)(x^3 - 2x + 3) = x^(1/2) (x^3 - 2x + 3)`
= `x^(7/2) - 2^(3/2) + 3x^(1/2)`
So `int sqrt(x)(x^3 - 2x + 3) "d"x = int x^(7/2) "d"x - int 2x^(3/2) "d"x + int 3x^(1/2) "d"x`
= `x^(7/2 + 1)/(7/2 + 1) - (2x^(3/2 + 1))/(3/2 + 1) + (3x^(1/2 + 1))/(1/2 + 1) + "c"`
= `2/9x^(9/2) - (2x^(5/2))/(5/2) + (3x^(3/2))/(3/2) + "c"`
= `2/9x^(9/2) - 4/5x^(5/2) + 2x^(3/2) + "c"`
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