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Question
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Solution
`int(2)/(sqrt(x) - sqrt(x + 3)).dx = int (2)/(sqrt(x) - sqrt(x + 3)) xx (sqrt(x) + sqrt(x + 3))/(sqrt(x) + sqrt(x + 3)).dx`
= `int(2(sqrt(x) + sqrt(x + 3)))/(x - (x + 3)).dx`
= `-(2)/(3) int(sqrt(x) + sqrt(x + 3)).dx`
= `-(2)/(3) int x^(1/2) dx - (2)/(3) int(x + 3)^(1/2).dx`
= `-(2)/(3).(x^(3/2))/((3/2)) - (2)/(3).((x + 3)^(3/2))/((3/2)) + c`
= `-(4)/(9)[x^(3/2) + (x + 3)^(3/2)] + c`
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