Question

difference between int(u^n)du and int(a^u)du?

Answer 1

let me ask u a question, what makes below functions different ?

\(\large f(x) = x^n\)

\(\large g(x) = a^x\)

Answer 2

the variable is above and the other one, not in the exponent

Answer 3

yes, the first one is called a `polynomial function`
and the second one is called a `exponential function`

Answer 4

ohhhhhh wait...so the a and n are both constants...0-0

Answer 5

you got it ! they're just constants

Answer 6

the differential "du" or "dx" tells you what the variable of integration is

Answer 7

Below is a polynomial in \(u\) :
\[\int (u^n)du\]

Answer 8

so it evaluates to :

\[\int (u^n)du = \dfrac{u^{n+1}}{n+1} + C\]

Answer 9

ahhhhhh ok and the other one is [ (ln a)^-1 ] [a^u]

Answer 10

Yep !

Answer 11

awesome thnx ^^

Answer 12

I like to write it like this :

\[\int (a^u)du = \dfrac{a^u}{\ln a} + C\]

Answer 13

u wlc :)