Question

hi, i'm having trouble with the integral of x/(2y+1)dy

Answer 1

I need to know the relationship between x and y for that to be done. Did you perhaps mean the following?\[\int \frac{y}{2y+1}dy\]

Answer 2

(Unless you intended x as a constant?)

Answer 3

nope, its a part of a larger question. i'm finding the double integral of (x^2 + x/(2y+1)). so to start it off i need to integrate the whole thing with respect to y so it would be (yx^2) for the first term, but i don't know how to do the second term (original question)

Answer 4

but, basically x is a constant to start with

Answer 5

use substitution, the integral of 1/u is ln u

Answer 6

alrighty, i was afraid i'd have to do that..

Answer 7

du is 2dx so you need to get a 2 there

Answer 8

wouldn't it be 2dy?

Answer 9

yes that's what i meant

Answer 10

HAHAHA "alrighty, i was afraid i'd have to do that.."

Answer 11

don't know if it'll work cuz of that first x^2 term..

Answer 12

you integrate the two terms seperately

Answer 13

ah ok

Answer 14

so the integral of x^2 is just x^2*y

Answer 15

\[\int {\frac{x}{{2y + 1}}dy = \frac{1}{2}x\int {\frac{2}{{2y + 1}}} } dy = \frac{1}{2}x\int {\frac{1}{u}} du = \frac{1}{2}x\ln u = \frac{1}{2}x\ln 2y + 1\]

Answer 16

thanks