Integrate:- dx/(x-?x)

Answers (1)

Let x=t^2
Differentiating, dx=2tdt
Putting the values,
x-sqrt x=t^2-t=t(t-1)
The given integral now becomes,
int frac1x-sqrt x dxRightarrow int frac1t(t-1)*2t*dt
int frac2(t-1)dt
Rightarrow 2*log (t-1)+K
Rightarrow 2*log (sqrt x-1)+K
Rightarrow log (x+1-2sqrt x)+K
where K is a constant.
 

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