Integration

[markosheehan]

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

[Guest]

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

Hope this helped,

R. Baber.

[markosheehan]

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

[Guest]

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

Hope this helped,

R. Baber.