# Integration

### Integration

how do you integrate e^X-e^-x/e^-x+1 dx
markosheehan

Posts: 12
Joined: Wed Jun 15, 2016 11:34 am
Reputation: 0

### Re: integration

$$\frac{e^x-e^{-x}}{e^{-x}+1}$$
$$= -1+\frac{e^x+1}{e^{-x}+1}$$
$$=-1+\frac{e^x(1+e^{-x})}{e^{-x}+1}$$
$$=-1+e^x$$
which should be easy to integrate.

Hope this helped,

R. Baber.
Guest

### Re: integration

how did you do this did you multiply by something or did you let -e^-1=1.

markosheehan

Posts: 12
Joined: Wed Jun 15, 2016 11:34 am
Reputation: 0

### Re: integration

There are many ways you could use to simplify the expression, one such way is to use the substitution $$u=e^x$$
So
$$\frac{e^x-e^{-x}}{e^{-x}+1}$$
$$=\frac{u-\frac{1}{u}}{\frac{1}{u}+1}$$
$$=\frac{(u-\frac{1}{u})\times u}{(\frac{1}{u}+1)\times u}$$
$$=\frac{u^2-1}{1+u}$$
$$=\frac{(u-1)(u+1)}{1+u}$$
$$=u-1$$
$$=e^x-1$$

Hope this helped,

R. Baber.
Guest