#1
Hate to start such a lame thread but does anyone know how to integrate y = a^x. I used to know the answer but I'm not sure I remember it right and I can't find it anywhere.

Cheers.
#4
Integrated it is (a^x+1)/x+1
Originally posted by TestForEcho
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#5
(1/x+1)a^(x+1)

I think.

If you differentiate it you get

1a^x

So I'm pretty sure it's right.


EDIT: Or you can put it like BadReligionRock did.
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#6
I'm not sure about that. I seem to remember that there was a standard formula where the answer involved logarithms.
#7
Quote by Herod
I'm not sure about that. I seem to remember that there was a standard formula where the answer involved logarithms.



Where you put "a", you don't mean what we see as "e" - as in the exponential function, do you?
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#8
Quote by Herod
I'm not sure about that. I seem to remember that there was a standard formula where the answer involved logarithms.


What I've shown you is right. Add one to the power, and divide by the new power.
Originally posted by TestForEcho
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#9
Isn't that what you'd do if it was x^a? You can't do that with a^x can you?
#10
a^x = e^ln(a^x) (as the e and ln will cancel each other.)
a^x = e^x * lna (standard log rules)
since lna is a constant, this can now be integrated the same method as e^kx

so your answer is 1/lna * e^xlna
=1/lna * a^x


for those confused, you cannot differentiat this in the same was as x^a, since x is a variable rather than a constant
#11
Quote by Herod
Isn't that what you'd do if it was x^a? You can't do that with a^x can you?


What's "a"? I assumed it was just another unknown variable.
Originally posted by TestForEcho
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#12
Quote by Badreligionrock
What's "a"? I assumed it was just another unknown variable.



We integrated with respect to a, not x
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#13
a is normally an Arbitrary constant, meaning its just a number. x is normally a variable, therefore it changes.
if a was a variable, it would mean you would need to use the product rule, and find da/dx too
#15
Ah well, this is why I study Accounting now and not Maths.
Originally posted by TestForEcho
Badreligionrock is the man.

Quote by Pinky19
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#16
haha anytime. i know how it feels to forget how to do a question like that.
#17
Quote by Herod
Isn't that what you'd do if it was x^a? You can't do that with a^x can you?

No
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#18
Quote by Badreligionrock
Integrated it is (a^x+1)/x+1


This, then add a constant as well I think, so ( (a^(x+1)) / (x+1) ) + C
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#19
Quote by The Overlord
This, then add a constant as well I think, so ( (a^(x+1)) / (x+1) ) + C



You're somewhat behind buddy
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