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

Quote by Pinky19
Badreligionrock you have the greatest avatar of all time. Rejected is the best video. Period.
(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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I'm not sure about that. I seem to remember that there was a standard formula where the answer involved logarithms.
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?
Co-President of UG's Tubgirl Virgins Club

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

Quote by Pinky19
Badreligionrock you have the greatest avatar of all time. Rejected is the best video. Period.
Isn't that what you'd do if it was x^a? You can't do that with a^x can you?
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

=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
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

Quote by Pinky19
Badreligionrock you have the greatest avatar of all time. Rejected is the best video. Period.
What's "a"? I assumed it was just another unknown variable.

We integrated with respect to a, not x
Co-President of UG's Tubgirl Virgins Club

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
l3vity FTW!

Cheers mate, that's really useful.
Ah well, this is why I study Accounting now and not Maths.
Originally posted by TestForEcho

Quote by Pinky19
Badreligionrock you have the greatest avatar of all time. Rejected is the best video. Period.
haha anytime. i know how it feels to forget how to do a question like that.
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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