Prove the inequality involving integrals How would you show that (if $x\gt0$):
$$\int_x^1 \frac{dt}{1 + t^2} = \int_1^{1/x} \frac{dt}{1 + t^2}$$
Hint

Make a change of variable $t=\frac {1} {u}$ on the left hand side and see what happens for the integral over $u$.
*put*$$ z=\frac{1}{t} $$ then the integrals limit changes and then omitting negative sign you get the answer