# Integration by substitution

1. Nov 10, 2009

### 3.141592654

1. The problem statement, all variables and given/known data

Integrate $$\int$$$$\frac{dz}{1+e^z}$$ by substitution

2. Relevant equations

3. The attempt at a solution

I chose u=(1+$$e^{z}$$) so du/dz=$$e^{z}$$ and dz=du/$$e^{z}$$.

Therefore, $$\int$$$$\frac{1}{u}$$ $$\frac{du}{e^{z}}$$

I plug z=ln(u-1) in for z, so $$\int$$$$\frac{1}{u}$$ $$\frac{du}{u-1}$$

From here though I don't know how to integrate. Can anyone help me with the next step?

2. Nov 10, 2009

### Staff: Mentor

Rewrite 1/(u(u -1)) as a sum: A/u + B/(u - 1). Solve for A and B so that the two expressions are identically equal. This is called partial fractions decomposition.