Expand : `(sqrt(t)-(1)/(sqrt(t)))^(3)`

int(1)/(sqrt(t))dt

int(dt)/( sqrt(t-1))

int(1)/(sqrt(t)+1)dt

int(dt)/( sqrt(1-t)-t)

int(4+sqrt(t))/(t^(3))dt

int sqrt(t)dt

int(dt)/(sqrt(3t-2t^2))

If e^x=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t))a and tany/2=sqrt((1-t)/(1+t)) ,then (dy)/(dx) at t=1/2 is (a) -1/2 (b) 1/2 (c) 0 (d) none of these

Let T = (1)/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7)) +(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)+2) then-

If S=[((sqrt(3)-1)/(2sqrt(2)),(sqrt(3)+1)/(2sqrt(2))),(-((sqrt(3)+1)/(2sqrt(2))),(sqrt(3)-1)/(2sqrt(2)))], A=[(1,0),(-1,1)] and P=S ("adj.A") S^(T) , then find matrix S^(T) P^(10) S .