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anonymous
 one year ago
evaluate the indefinite integral
integral of (6)/(e^(8x))dx
anonymous
 one year ago
evaluate the indefinite integral integral of (6)/(e^(8x))dx

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits \frac{ 6 }{ e ^{8x} }dx\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can i use u substitution?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so if i make u=e^(8x) my du would be 1/8du = e^(8x)dx

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so then i would have 1/8 integral of 6/u ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not sure if i am right so far

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is it possible to take out the u from the bottom?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is it true that if i take out u from the bottom of the fraction it would become u^(1) ?

Empty
 one year ago
Best ResponseYou've already chosen the best response.2You're on the right track you'll need a substitution I think! I'll help walk you through this, first let's take out the coefficient 6 and use exponent rules to rewrite it like this: \[6 \int e^{8x}dx\] From here you can use this substitution: \[u=8x \] Take the derivative of this to get: \[\frac{du}{dx} = 8\] multiply \(dx\) by both sides: \[du=8dx\] divide 8 from both sides: \[\frac{1}{8} du = dx\] Now you can plug these into your for \(8x=u\) and \(\frac{1}{8}du = dx\) \[6 \int e^u * \frac{1}{8} du\] Pull this constant out as well to get \[\frac{6}{8} \int e^udu\] Now see if you can take it from here.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you i will try it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the integral will be e^(u+1)/(u+1) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and i plug in u back in now which is 8x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so my answer is (e^(8x+1))/((8x+1)+1)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hmm i think i did it wrong that answer is not correct

Empty
 one year ago
Best ResponseYou've already chosen the best response.2So what you're doing is the rule for polynomials: \[\int x^n dx = \frac{x^{n+1}}{n+1}\] but the type of integral you're looking at is: \[\int e^x dx = e^x\] Which you can check by taking the deriativatives of the right hand sides of the equations since integrals are antiderivatives

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh i see, so the integral of e^u is just e^u... and all i would have to do is plug in my u and multiply it by 6/8 ...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so my answer is 3/4e^(8x)

Empty
 one year ago
Best ResponseYou've already chosen the best response.2Awesome glad I could help!
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