Question

How do you find the indefinite integral of [(1+e^x)^2]/e^x?

Answer 1

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

Answer 2

So you have:
\[\int\limits \frac{(1+e^x)^2}{e^x}dx\]

Answer 3

\[\int\limits \frac{(1+e^x)^2}{e^x}dx\]\[\int\limits\frac{1+2e^x+e^{2x}}{e^x}dx=\int\limits e^{-x}dx+\int\limits 2dx +\int\limits e^xdx\]

Answer 4

Multiply the top out. Then divide the e^x through leaving:
\[\int\limits \frac{1+2e^x+e^{2x}}{e^x}dx=\int\limits [e^{-x}+2+e^x]dx\].

Answer 5

-e^x+2x+e^x=2x+2sinhx

Answer 6

Then from there its straight forward:
I=-e^-x+2x+e^x+c=2x+2sinh(x)+c

Answer 7

Haha, at least I wasn't the only one noticing the hyperbolic trig :D

Answer 8

Make sense blue?

Answer 9

I get that, thanks :D

Answer 10

:D