Deriving the Integral via Leibniz Rule

[dirk_mec1]

Homework Statement

<br /> \int_0^1\frac{x-1}{\ln{x}} dx<br />

Homework Equations

<br /> \Phi(\alpha)=\int_0^1\frac{x^{\alpha}-1}{\ln{x}} dx<br />

The Attempt at a Solution

In the answers they say:<br /> \Phi &#039;(\alpha)=\int_0^1\frac{x^{\alpha}\ln{x}}{\ln{x}} dx=\frac{1}{\alpha+1}<br />but the derative is wrong, right? I don't understand how they calculated the derative...

 

[Dick]

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

 

[dirk_mec1]

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

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