e^(-x)/(5+e^(-x))^2?

Question

How to integrate e^(-x) / (5+e^(-x))^2 dx ?
I just take 5+e^-x=y
so,-e^(-x)dx = dy or e^(-x)dx = - dy .
but i cold not complete.Please give a solution.

Answer 1

u use e^(-x)dx=-dy in the integral like so:
-(e^(-x)dx)/(5+e^(-x))^2 = -dy/y^2
when u integrate it, it becomes

1/y + c, that is 1/e^(-x) +c

and that's it! easy...

Answer 2

So you got the integral of -dy/y^2, right? That is just -y^(-2) dy, which integrates to y^(-1)=1/y+C. Now you can finish.

Answer 3

first make -(-e^(-x))/(5+e^(-x))^2

then u'll realise that when u differentiate 1/(5+e^(-x))^2 you get (-e^(-x))/(5+e^(-x))^2

so which means that if u integrate (-e^(-x))/(5+e^(-x))^2 you'll get back 1/(5+e^(-x))^2

but since u have an extra - sign so u'll get -1/(5+e^(-x))^2, which is the ans that u're looking for

Answer 4

Take up less math and more spelling.