Integration by partial fractions part. 2

[sdoyle]

Homework Statement

$$\int\frac{e^x}{(e^x-2)(e^2x +1)}$$ it should be e to the power of 2x

Homework Equations

Using substitution u=e^x, and then using partial fractions

The Attempt at a Solution

I have done this problem two separate ways. One with substitution and then partial fractions, and the other with just partial fractions. Both times I end with different coefficient values. I'm not sure if you can use both substitution and then partial fractions...

 

[mistermath]

In your equation (which I can't really read) you're missing the dx! What I recommend you do is a u substitution, but make sure you change all the things related to x to u. For example, u = e^x, then du = e^x * dx so when you substitute the e^2x on top becomes e^x (since one of them is used for the du) giving you:

(u du) / [(u-2)(u^2 + 1)]