6sqrt(sqrt(ax+8))dx

int_2^6 sqrt(8-x)/(sqrtx+sqrt(8-x))dx equals :

int(dx)/(sqrt(x)+sqrt(x-8))

int ((log(1+6sqrt(x)))/(3sqrt(x)+sqrt(x))+(1)/(3sqrt(x)+4sqrt(x)))dx

int(sqrt(x))/(sqrt(x)+sqrt(6-x))dx

int(sqrt(a)-sqrt(x))/(1-sqrt(ax))dx

Factorize 6+2sqrt(3)-sqrt(8)-2sqrt(6)

The value of (1)/(sqrt(4)+sqrt(5))+(1)/(sqrt(5)+sqrt(6))+(1)/(sqrt(6)+sqrt(7))+(1)/(sqrt(7)+sqrt(8))+(1)/(sqrt(8)+sqrt(9)) is

(1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+(1)/(sqrt(4)+sqrt(5))+(1)/(sqrt(5)+sqrt(6))+(1)/(sqrt(6)+sqrt(7))+(1)/(sqrt(7)+sqrt(8))+(1)/(sqrt(8)+sqrt(8))

If y =tan ^(-1) ((sqrt( a) -sqrt(x)) /( 1+sqrt( ax)) ) ,then (dy)/(dx)=