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If int (x+1)/(sqrt(2x-1))dx=f(x) sqrt(2x...

If `int (x+1)/(sqrt(2x-1))dx=f(x) sqrt(2x-1)+C`, where C is a constant of integration, then f(x) is equal to

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The correct Answer is:
3
`int (x +1)/(sqrt2 x -1) dx`
Let `2x -11= t ^(2) implies 2 dx=2t dt`
`int ((t^(2)+ 1)/(2)+1)/(t)xx t dt implies 1/2 int (t ^(2) + 3) dt`
`1/3[ (t ^(3))/(3) + 3t] + C = (t ^(3))/(6) + 3/2t +C = ((2x-1 )^(3//2))/(6 ) + 3/2 (2x-1)^(1//2)+C= (2x-1)^(1//2)((x +4)/(3))+C`
`therefore f (x) = (x+4)/(3).`
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