Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
intergrate (2^x)/((2^x +1)^2) dx?
use the substition u=2^x please show ALL working as im not very good at this
doing it on paper and scanning the image would help lots!!!!
i will give you best answer if you make me understand
1 Answer
- kbLv 71 decade agoFavorite Answer
Let u = 2^x. So, du = 2^x * ln 2 dx ==> 2^x dx = (1/ln(2)) * du.
So, we get u/(u+1)^2 * (1/ln(2)) du.
In order to integrate this, use another substitution.
Let w = u +1, u = w -1, du = dw.
So, we get
(w-1)/w^2 * (1/ln(2)) dw =
(1/ln(2)) * (w^(-1) - w^(-2)) dw =
(1/ln(2)) * (ln|w| + w^(-1)) + C
Since w = u + 1 = 2^x + 1, our final answer is
(1/ln(2)) * [ln(2^x + 1) + (2^x + 1)^(-1)] + C.
I dropped the absolute value bars, because 2^x + 1 is never negative.
