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

1. ## How To Solve Integral of e? And solve velocity?

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

ln |e^x - 1| + c

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

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

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?

2. 1) $\int \frac {1}{1-e^{-x}} \ dx = \int \frac {1}{1-e^{-x}} \frac {e^{x}}{e^{x}} \ dx$ = $\int \frac {e^{x}}{e^{x}-1} \ dx$
2) hint: $e^{x-y} = \frac {e^{x}}{e^{y}}$