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anonymous
 one year ago
Find thw antiderivative of
\[f(x)=\frac{ 1 }{ x^2 }e ^{1/x}\]
anonymous
 one year ago
Find thw antiderivative of \[f(x)=\frac{ 1 }{ x^2 }e ^{1/x}\]

This Question is Closed

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.6\[\large \int \frac{e^{1/x}}{x^2}\] Make a usub of 1/x

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.6Oh...what have you learned?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How do you write in this format? f(x)=F(x)+C

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0\[\Large\rm \int\limits f(x)dx=F(x)+C\]Where F(x) is the antiderivative of f(x). Did you understand the usubstitution?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is there another way to solve it without using the usubstitution?

freckles
 one year ago
Best ResponseYou've already chosen the best response.0i can't think of a better way

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The reason that I ask that was because the question was at the beginning of antiderivatives/integration. I learned the usubstitution as a last topic...

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0you may use advanced guessing what is the derivative of \(\large e^{1/x}\) ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0what do you know about chain rule

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Chain rule applies to composite function. It describe of outer evulated at inner, times derivative of inner

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.6So using that logic...if we consider the "inner" as 1/x The derivative of \(\large e^{1/x}\) would be \(\large \frac{d(1/x)}{dx} \times e^{1/x}\) So what is the derivative of \(\large 1/x\) ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.0you found the antiderivative for positive x

freckles
 one year ago
Best ResponseYou've already chosen the best response.0that you found the antiderivative of 1/x for positive x the question was to differentiate

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0derivative if lnx is 1/x derivative of 1/x is not lnx

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ooh... derivative of 1/x is 1/x^2 ...

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.6Correct...and to finish up from the previous post \[\large \frac{d}{dx}e^{1/x} = e^{1/x} \times \frac{d}{dx}\frac{1}{x}\] Since we just found the later \(\large \frac{d}{dx} \frac{1}{x} = \frac{1}{x^2}\) we have \[\large \frac{d}{dx}e^{1/x} = \frac{e^{1/x}}{x^2}\] right? Now what do you notice?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So F(x)= e^{1/x} +C ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you! :) I got it now. I was messed up b/w derivatives and antiderivatives. My bad...

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.6Yeah sometimes they can be hard to keep straight...but as long as you can derive them you're all set!
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