What Is the Best Way to Solve Integrals Involving Exponential Functions?

[Saladsamurai]

because I keep getting jammed up here,

Using u substitution

\int \frac{dx}{e^x} I don't see what else to let u equal besides e^x. ...

 

[learningphysics]

Take the denominator to the top...

 

[Saladsamurai]

Take the denominator to the top...

I just got it I think...Like I said, somehow since last night I've lost brain cells! for some reason I wouldn't believe that d\dx [e^-x]=e^-x <---
that is correct though right?
what is the derivative of e^-x ?

 

[learningphysics]

I just got it I think...Like I said, somehow since last night I've lost brain cells! for some reason I wouldn't believe that d\dx [e^-x]=e^-x <---
that is correct though right?

almost. be careful about the '-'

You should use the chain rule: what is the derivative of e^(ax)

 

[Saladsamurai]

almost. be careful about the '-'

You should use the chain rule: what is the derivative of e^(ax)

is it ae^ax ?

so it should be -e^{-x}

 

[Saladsamurai]

Just checked the answer and it is right. Thanks. Strange that I forgot to chain rule.

 

[learningphysics]

Just checked the answer and it is right. Thanks. Strange that I forgot to chain rule.

no prob.