Subtask 1

´int 1/sqrt(x) dx´

The integral of ´1/sqrt(x)´ is ´2 sqrt(x)´: ´= 2 sqrt(x) + "constant"´

´int_0^1 dx/sqrt(x) = (2 sqrt(1) + "constant") - (2 sqrt(0) + "constant") = 2´

Subtask 2

´int 1/(x-1)^2 dx´

For the integrand ´1/(x-1)^2´, substitute ´u = x-1´ and ´du = dx´: ´= int 1/u^2 du´

The integral of ´1/u^2´ is ´-1/u´: ´= -1/u + "constant"´

Substitute back for ´u = x-1´: ´= 1/(1-x) + "constant"´

´int_1^2 dx/(x - 1)^2 =´ The Integral does not converge!

Subtask 3

´int 1/x^2 dx = -1/x + "constant"´

´int_1^oo dx/x^2 = 1´