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Integrate the functions(x+2)/(sqrt(x^2-1...

Integrate the functions`(x+2)/(sqrt(x^2-1))`

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` int (x+2)/(sqrt(x^(2)-1))dx " " underset(rArr x dx = t dt)underset(rArr 2x dx = 2t dt)underset(" Let " x^(2) -1=t^(2))(" for first integral")`
` =int (x)/(sqrt(x^(2)-1))dx +2 int (1)/(sqrt(x^(2)-1))dx`
` = int (tdt)/(sqrt(t^(2)))+2 int (1)/(sqrt(x^(2)-1^(2)))dx`
`=int 1dt +2 int (1)/(sqrt(x^(2)-1^(2)))dx`
` = t+ 2 log |x+sqrt(x^(2) -1^(2))|+c`
` =sqrt(x^(2)-1) + 2log |x+ sqrt(x^(2)-1)|+c`
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