Chapter 8.1, Problem 80E

Skydiving A skydiver in free fall subject to gravitational acceleration and air resistance has a velocity given by $v(t)=v_T\left(\frac{e^{at}-1}{e^{at}+1}\right)$, where v_T is the terminal velocity and a > 0 is a physical constant. Find the distance that the skydiver falls after t seconds, which is $d(t)={\displaystyle {\int }_0^{t}v(y)dy}$.