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Integrate the following functions with r...

Integrate the following functions with respect to x .
(i) `sqrt(9-(2x+5)^2)`
(ii) `sqrt(81+(2x+1)^2)`
(iii) `sqrt((x+1)^2-4)`

Text Solution

Verified by Experts

The correct Answer is:
(i) `1/4[(2x+5)sqrt(9-(2x+5)^2)+9sin^(-1)""((2x+5)/3)]+c`
(ii) `1/4[(2x+1)sqrt(81-(2x+1)^2)+81log|(2x+1)+sqrt(81+(2x+1)^2)|]+c`
(iii) `((x+1)/2)sqrt((x+1)^2-4)+2log|(x+1)+sqrt((x+1)^2-4)+c`
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