Question

I have a total brain fart, how do you integrate e^-x? Step by step please.

Answer 1

\[\int\limits {e^{-x}}dx = \frac{e^{-x}}{-1}=-e^{-x}\]

Answer 2

Think the Anti-Derivative way

Answer 3

When we differentiate \(e^x\) we get \(e^x\)

Answer 4

I know that when u take the anti-derivative you add instead of subtract, but that x is throwing me off

Answer 5

\(e^{-x}\) derivative is \( -e^{-x}\)

Answer 6

But in the problem we have to find the integral or anti-derivative of \(e^{-x}\) so If I add another - thing should work

Answer 7

u=-x
du=-dx
dx=-du

\[\int\limits {e^u (-du)} = -\int\limits{e^udu} = -e^u = -e^{-x}\]

Answer 8

If I differentiate \(-e^{-x}\) I will have \(-(-e^{-x})\) ....

Answer 9

Oh, I see now. The U substitution really helped. Thank you so very much, this was driving me nuts.

Answer 10

I havent done simple calculus in a while so I am really rusty. Thanks again.

Answer 11

@ upilson yeh because
\[\frac{d}{dx}( e^{f(x)}) = f '(x) e^{f(x)}\]

Answer 12

ur welcome:)