## anonymous one year ago My Achilles heel...

1. anonymous

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2. phi

you could write 3 as $$e^{\ln3 }$$

3. anonymous

I cant find that in my equation page..

4. anonymous

what happends to x?

5. anonymous

So how would u go on from there?

6. phi

use $\left(a^b\right)^c = a^{bc}$

7. phi

$\int 3^x \ dx = \int \left(e^{\ln3}\right)^x \ dx\\ = \int e^{\ln 3 \ x} \ dx$

8. phi

which is in the form $\int e^{ax} \ dx$

9. anonymous

ok please continue, Ive had problem with these types, but ur explanation makes it easier.

10. phi

can you integrate $\int e^{ax} \ dx$ ? this is a "standard" integral

11. anonymous

Ive forgotten

12. phi

what is the derivative of e^x ?

13. anonymous

I have a problem with math, if I dont keep doing it, I fforget it..

14. phi

this one is worth looking up

15. anonymous

okey, I will go through that chapter again...can u guide me through this one?

16. phi

$\frac{d}{dx} e^{a x}= e^{ax} \frac{d}{dx} ax = a\ e^{ax}$

17. phi

your problem is to "undo that" in other words $\int e^u \ du$ where u = ax $du = a \ dx$

18. phi

and $\int e^u \ du = e^u$

19. anonymous

ok, I will have to go through this chapter again, I seem to be forgetting..also Im tired, thank you !:)

20. 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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