`int_(1)^(2)(dx)/(sqrtx-sqrt(x-1))`

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The correct Answer is:

`(4sqrt2)/(3)`

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Evaluate the definite integrals int_(0)^(1)(dx)/(sqrt(1+x)-sqrtx)

By using the properties of definite integrals, evaluate the integrals int_(0)^(a)(sqrtx)/(sqrtx+sqrt(a-x))dx

int_(0)^(a)(sqrtx)/(sqrt(x) + sqrt(a-x))dx .

If int_0^1 (dx)/(sqrt(1 + x) - sqrt(x)) =(ksqrt(2))/(3) , then k is :

int_a^(b) (sqrtx dx)/(sqrtx + sqrt(a+b-x)) =

int_(1)^(sqrt3) (dx)/(sqrt(4 - x^2)) is :

int_(0)^(1//2)(dx)/((1+x^(2))sqrt(1-x^(2))) is equal to

int_(1)^(3)(sqrt(4-x))/(sqrt(x)+sqrt(4-x))dx=

int_0^(1/2) (dx)/(sqrt(1-x^(2))) =

int (1+x+sqrt(x+x^(2)))/(sqrtx + sqrt(1+x)) dx =