anonymous
  • anonymous
My Achilles heel...
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
|dw:1439212533266:dw|
phi
  • phi
you could write 3 as \( e^{\ln3 } \)
anonymous
  • anonymous
I cant find that in my equation page..

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anonymous
  • anonymous
what happends to x?
anonymous
  • anonymous
So how would u go on from there?
phi
  • phi
use \[ \left(a^b\right)^c = a^{bc} \]
phi
  • phi
\[ \int 3^x \ dx = \int \left(e^{\ln3}\right)^x \ dx\\ = \int e^{\ln 3 \ x} \ dx \]
phi
  • phi
which is in the form \[ \int e^{ax} \ dx \]
anonymous
  • anonymous
ok please continue, Ive had problem with these types, but ur explanation makes it easier.
phi
  • phi
can you integrate \[ \int e^{ax} \ dx \] ? this is a "standard" integral
anonymous
  • anonymous
Ive forgotten
phi
  • phi
what is the derivative of e^x ?
anonymous
  • anonymous
I have a problem with math, if I dont keep doing it, I fforget it..
phi
  • phi
this one is worth looking up
anonymous
  • anonymous
okey, I will go through that chapter again...can u guide me through this one?
phi
  • phi
\[ \frac{d}{dx} e^{a x}= e^{ax} \frac{d}{dx} ax = a\ e^{ax}\]
phi
  • phi
your problem is to "undo that" in other words \[ \int e^u \ du \] where u = ax \[ du = a \ dx\]
phi
  • phi
and \[ \int e^u \ du = e^u \]
anonymous
  • anonymous
ok, I will have to go through this chapter again, I seem to be forgetting..also Im tired, thank you !:)
Loser66
  • Loser66
Trick: to find \(\int 3^x dx\), we need find "something" whose derivative = \(3^x\), right? let see, \((3^x)'= 3^x ln 3\) not \(3^x\), but ln3 is a constant, so, we just divide the original one by ln3. I meant \((\dfrac{3^x}{ln3})' = (\dfrac{1}{ln3} *3^x)'= \dfrac{1}{\cancel{ln3}}3^x *\cancel{ln3}=3^x\) hence \(\int 3^x dx = \dfrac{3^x}{ln3}+C\)

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