# Homework Help: Integration via Leibniz

1. Feb 19, 2009

### dirk_mec1

1. The problem statement, all variables and given/known data
$$\int_0^1\frac{x-1}{\ln{x}} dx$$

2. Relevant equations
$$\Phi(\alpha)=\int_0^1\frac{x^{\alpha}-1}{\ln{x}} dx$$

3. The attempt at a solution

$$\Phi '(\alpha)=\int_0^1\frac{x^{\alpha}\ln{x}}{\ln{x}} dx=\frac{1}{\alpha+1}$$

but the derative is wrong, right? I don't understand how they calculated the derative...

2. Feb 19, 2009

### Dick

The derivative is d/d(alpha). x^alpha=e^(log(x)*alpha). Actually, it is right.

3. Feb 19, 2009

### dirk_mec1

You're right I accendentally differentiated w.r.t x, thanks Dick.