# Simple integral

this integral can be solved without u-subsitution however, I get a different answer when I use u-sub.

$$\int \frac{6}{x-6} dx$$

$$u=x-6$$

$$du=dx$$

$$\int \frac{1}{6u}=\frac{1}{6}ln(x-6)$$

if U-sub wasnt used, then the answer would be 6ln(x-6)

what am I doing wrong in the subsitution?

James R
Homework Helper
Gold Member
With the substitution, the integral is:

$$\int \frac{6}{u} du$$

not

$$\int \frac{1}{6u} du$$