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Question
Evaluate : `int_3^5 (1)/(sqrt(2x + 3) - sqrt(2x - 3))*dx`
Solution
`int_3^5 (1)/(sqrt(2x + 3) - sqrt(2x - 3))*dx`
= `int_3^5 (1)/(sqrt(2x + 3) - sqrt(2x - 3)) xx (sqrt(2x + 3) + sqrt(2x - 3))/(sqrt(2x + 3) + sqrt(2x - 3))*dx`
= `int_3^5 (sqrt(2x + 3) + sqrt(2x - 3))/((2x + 3) - (2x - 3))*dx`
= `(1)/(6) int_3^5 (2x + 3)^(1/2)*dx + (1)/(6) int_3^5 (2x - 3)^(1/2)*dx`
= `(1)/(6)[(2x + 3^(3/2))/(2(3/2))]_3^5 + (1)/(6)[((2x - 3)^(3/2))/(2(3/2))]_3^5`
= `(1)/(18)[(10 + 3)^(3/2) - (6 + 3)^(3/2)] + (1)/(18)[(10 - 3)^(3/2) - (6 - 3)^(3/2)]`
= `(1)/(18)[13sqrt(13) - 9sqrt(9)] + (1)/(18)[7sqrt(7) - 3sqrt(3)]`
= `(1)/(18)(13sqrt(13) - 27 + 7sqrt(7) - 3sqrt(3))`
= `(1)/(18)(13sqrt(13) + 7sqrt(7) - 3sqrt(3) - 27)`.
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