Question

int 5/(e^x-2)

Answer 1

Is it \[\int \frac{5}{e^{x-2}}dx \]or \[ \int \frac{5}{e^x - 2}dx\]?

Answer 2

\[\huge \int \frac{5}{e^{x^{-2}}}\]

just wanted to type it :p

Answer 3

oops typo should be 3e(^x)-2

Answer 4

so the second one with 3 in front

Answer 5

\[\LARGE \int \frac{5}{3e^x - 2}dx?\]

Answer 6

yup

Answer 7

that makes things easier

Answer 8

I think the catch here is to make u = e^x, du = e^xdx, so dx = du/u and then partial fractions.

Answer 9

Partial fractions on: \[ \int \frac{5}{(3u - 2)u}du\]

Answer 10

why the extra u in the denominator?

Answer 11

dx = du/u

Answer 12

u = e^x, du = e^x dx, solve for dx: dx = du/e^x. But e^x = u, so dx = du/u

Answer 13

yep.