Hello,
I need help integrating this function:
e^x/ (1+e^x)^2
Its not a homework I just havent done intergal in a while and dont remember how to do it. Can someone help me.

Question

Hello, 
I need help integrating this function:
e^x/ (1+e^x)^2
Its not a homework I just havent done intergal in a while and dont remember how to do it. Can someone help me.

anonymous · Answer

Make the change of variable
$$u= 1+ e^x\
du = e^x dx
$$

anonymous · Answer

Don't remember how to do it.

anonymous · Answer

The integral becomes
$$
\int \frac { du} { u^2}= -\frac 1 u + C =  -\frac 1 {1+e^x} + C
$$

anonymous · Answer

Ok, I tried it and got the same thing so that is the final answer right? no more changes to make to it? Thanks eliassaab!

anonymous · Answer

Yes, you are done if you did it as in my post above.

anonymous · Answer

hello,
can someone help me to put u in terms of x please:
a=parameter
exp(x)=e^x
a*exp(-x)*((exp(-exp(-x)))^a)=u
Meant to find x in terms of u. so the form x="..."

anonymous · Answer

Hi,
Anyone know how to differentiate this for example. 4^x ?
a constant (4) to the power of x. Would appreciate some help.

anonymous · Answer

$$4^x \ln(4)$$

anonymous · Answer

If there are 2 elements A and B among a total of N elements and I draw a bunch
of size 'n' one element after the other without replacement , what is the probability that only A is selected but not B. in terms of n and N. Anyone want to tackle this one please?