Question

hii
$\frac{dx}{x - \sqrt{x} }$
​

Answer 1

Answer:

2 log ( √x + 1 ) + c

Step-by-step explanation:

To find ---> ∫ dx / ( x - √x )

Solution---> We have some formulee of differentiation and intreation as follows,

1) d / dx ( √x ) = 1 / 2√x

2) ∫ 1 / x dx = logx

We apply these formulee in evaluating the intregation.

∫ dx / ( x - √x )

= ∫ dx / ( √x √x - √x )

Taking √x common from denominator , we get ,

= ∫ dx / √x ( √x - 1 )

Let , √x -1 = t

=> ( 1 / 2√x - 0 ) dx = dt

=> ( 1 / √x ) dx = 2 dt

Now ,

∫ 2 dt / t

= 2 ∫ dt / t

= 2 logt + c

= 2 log ( √x + 1 ) + c