dstefan
03-22-2008, 01:03 PM
Chapter 1, Problem 2:
Compute \int \frac{1}{x \ln(x)} dx using the substitution u = \ln(x).
Solution:
du = \frac{dx}{x} and therefore
\int \frac{1}{x \ln(x)} dx = \int \frac{1}{u} du = \ln(|u|) = \ln(|\ln(x)|) + C.
Compute \int \frac{1}{x \ln(x)} dx using the substitution u = \ln(x).
Solution:
du = \frac{dx}{x} and therefore
\int \frac{1}{x \ln(x)} dx = \int \frac{1}{u} du = \ln(|u|) = \ln(|\ln(x)|) + C.