Evaluate the integral.
$ \int_{1}^{\infty} \frac{d x}{x \ln x} $
A) $ \frac{1}{2} $
B) $ -\frac{1}{2} $
C) $ -\frac{1}{4} $
D) $ \frac{1}{4} $
E) divergent

Question

Quizplus · Accepted Answer

The integral $ \int_{1}^{\infty} \frac{d x}{x \ln x} $ diverges because the integrand behaves like $ \frac{1}{x} $ near $ x = 1 $ and $ \ln x \to \infty $ as $ x \to \infty $, leading to divergence.

Evaluate the Integral ∫1∞dxxln⁡x \int_{1}^{\infty} \frac{d x}{x \ln x} ∫1∞​xlnxdx​ A) 12 \frac{1}{2} 21​

Evaluate the Integral $\int_{1}^{\infty} \frac{d x}{x \ln x}$ A) $\frac{1}{2}$