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

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In summary, the conversation discusses using u-substitution to solve the integral of 1/e^x and the derivative of e^-x using the chain rule. The conversation also mentions a mistake with the negative sign in the derivative.
  • #1
Saladsamurai
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because I keep getting jammed up here,

Using u substitution

[tex]\int \frac{dx}{e^x}[/tex] I don't see what else to let u equal besides e^x. ...
 
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  • #2
Take the denominator to the top...
 
  • #3
learningphysics said:
Take the denominator to the top...

I just got it I think...Like I said, somehow since last night I've lost brain cells!:grumpy: 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 ?
 
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  • #4
Saladsamurai said:
I just got it I think...Like I said, somehow since last night I've lost brain cells!:grumpy: 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)
 
  • #5
learningphysics said:
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 [tex]-e^{-x}[/tex]
 
  • #6
Just checked the answer and it is right. Thanks. Strange that I forgot to chain rule.
 
  • #7
Saladsamurai said:
Just checked the answer and it is right. Thanks. Strange that I forgot to chain rule.

no prob.
 

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