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Question
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
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Solution
Let I = `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
`= -2 int 1/(sqrt("5x" - 4) - sqrt("5x" - 2)) xx (sqrt("5x" - 4) + sqrt("5x" - 2))/(sqrt("5x" - 4) + sqrt("5x" - 2))`dx
`= - 2 int (sqrt("5x" - 4) + sqrt("5x" - 2))/(("5x" - 4) - ("5x" - 2))` dx
`= -2 int (sqrt("5x" - 4) + sqrt("5x" - 2))/-2` dx
`= int [("5x" - 4)^(1/2) + ("5x" - 2)^(1/2)]`dx
`= int ("5x" - 4)^(1/2) "dx" + int ("5x" - 2)^(1/2)` dx
`= ("5x" - 4)^(3/2)/(3/2) xx 1/5 + ("5x" - 2)^(3/2)/(3/2) xx 1/5` + c
∴ I = `2/15 [("5x" - 4)^(3/2) + ("5x" - 2)^(3/2)]` + c
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