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Question
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Solution
Let I = `int (x - 2)^2 sqrt(x)*dx`
= `int (x^2 - 4x + 4)sqrt(x)*dx`
= `int (x^(5/2) - 4x^(3/2) + 4x^(1/2))*dx`
= `int x^(5/2)*dx - 4 int x^(3/2)*dx + 4 int x^(1/2)*dx`
= `x^(7/2)/((7/2)) - 4 x^(5/2)/((5/2)) + 4 x^(3/2)/((3/2))`
= `(2)/(7)x^(7/2) - 8/5x^(5/2) + (8)/(3)x^(3/2) + c`.
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