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Question
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Solution
`int(3x^3 - 2x + 5)/(xsqrt(x))dx`
= `intx^((-3)/(2))(3x^3 - 2x + 5)dx`
= `int(3x^(3/2) - 2x^(-1/2) + 5x^(-3/2))dx`
= `3intx^(3/2)dx - 2intx^(-1/2) dx + 5int x^(-3/2)dx`
= `3(x^(3/2 + 1)/(3/2 + 1)) - 2(x^(1/2 + 1)/(-1/2 + 1)) + 5(x^(-3/2 + 1)/(-3/2 + 1)) + c`
= `(6)/(5)x^2sqrt(x) - 4sqrt(x) - (10)/sqrt(x) + c`.
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