Displacement under varying acceleration

[MechaMZ]

Homework Statement

A 7.00 kg object starting from rest falls through a viscous medium and experiences a resistive force = -b , where is the velocity of the object. The object reaches one half its terminal speed in 6.14 s.

terminal speed = 86.898m/s

How far has the object traveled in the first 6.14 s of motion?

The Attempt at a Solution

i don't understand why i couldn't simply use an integration of V to find the displacement since the acceleration is not constant.

the method I've tried.
v=v_t(1-e^(-t/T))
T=m/b
=7/b
=v_t/9.81
v=86.898(1-e^(-t/8.858))

$$\int^{t=6.14}_{t=0}$$ v_t(1-e^(-t/T))dt
$$\int^{t=6.14}_{t=0}$$ (86.898-86.898e^-t/8.858)dt
533.55-(43.448-86.898)
577m

my answer is wrong, but i don't know why it is wrong. hope somebody could explain to me

 

[Fightfish]

Check your definite integration - the numbers look funny.

 

[MechaMZ]

where it goes wrong?

 

[Fightfish]

$$\int 86.898 - 86.898 e^{-t/8.858} dt = 86.898t + (8.858) 86.898 e^{-t/8.858} + C$$
I can't tell exactly where you went wrong since your integration process and final integrated form is not shown, but from your values, it seems that you must have messed up the integration of the exponential part.