Thread: How To Solve Integral of e? And solve velocity?

1) int(1/(1-e^(-x)))
My attempt:
ln |1-e^(-x)| + c

Answer:
ln |e^x - 1| + c

2) Solve the differential equation:
(e^(x-y))dy=-dx

My Attempt:
-1/(e^(x-y))=dy/dx

Answer:
0 = e^(-y) + e^(-x) + c

3) a(t) = -32 ft/s as the acceleration due to gravity. An object is vertically thrown downward from the top of the 480 foot building with an initial velocity of 64 ft/s. With what velocity does the object hit the ground?

My Attempt:
int(-32) = -32x + c
v = -32x + 480?

Answer:
v = -186.56 ft/sec

1) =


2) hint: