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Question
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
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Solution
`int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
= `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)) xx (sqrt(7x - 2) + sqrt(7x - 5))/(sqrt(7x - 2) + sqrt(7x - 5)).dx`
= `int (3(sqrt(7x - 2) + sqrt(7x - 5)))/((7x - 2) - (7x - 5)).dx`
= `int (sqrt(7x - 2) + sqrt(7x - 5)).dx`
= `int(7x - 2)^(1/2) .dx + int(7x - 5)^(1/2).dx`
= `((7x - 2)^(3/2))/(3/2) xx (1)/(7) + ((7x - 5)^(3/2))/(3/2) xx (1)/(7) + c`
= `(2)/(21)(7x - 2)^(3/2) + (2)/(21)(7x - 5)^(3/2) + c`.
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