anonymous
  • anonymous
evaluate the indefinite integral integral of (6)/(e^(8x))dx
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\int\limits \frac{ 6 }{ e ^{8x} }dx\]
anonymous
  • anonymous
can i use u substitution?
anonymous
  • anonymous
so if i make u=e^(8x) my du would be 1/8du = e^(8x)dx

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anonymous
  • anonymous
so then i would have 1/8 integral of 6/u ?
anonymous
  • anonymous
not sure if i am right so far
anonymous
  • anonymous
is it possible to take out the u from the bottom?
anonymous
  • anonymous
is it true that if i take out u from the bottom of the fraction it would become u^(-1) ?
Empty
  • Empty
You'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
  • anonymous
thank you i will try it
anonymous
  • anonymous
so the integral will be e^(u+1)/(u+1) ?
anonymous
  • anonymous
and i plug in u back in now which is -8x
anonymous
  • anonymous
so my answer is (e^(-8x+1))/((-8x+1)+1)
anonymous
  • anonymous
hmm i think i did it wrong that answer is not correct
Empty
  • Empty
So 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
  • anonymous
oh 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
  • anonymous
so my answer is -3/4e^(-8x)
anonymous
  • anonymous
thank you!
Empty
  • Empty
Awesome glad I could help!

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