# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int_1^{\infty}\left(\frac{ln\left(x^2\right)}{x}\right)dx$

Learn how to solve definite integrals problems step by step online.

$\lim_{c\to\infty }\:\int_{1}^{c}\frac{\ln\left(x^2\right)}{x}dx$

Learn how to solve definite integrals problems step by step online. Integrate (ln(x^2)/x from 1 to \infty. Replace the integral's limit by a finite value. Solve the integral \int_{1}^{c}\frac{\ln\left(x^2\right)}{x}dx applying u-substitution. Let u and du be. Isolate dx in the previous equation. Substituting u and dx in the integral and simplify.

The integral diverges.

### Problem Analysis

$\int_1^{\infty}\left(\frac{ln\left(x^2\right)}{x}\right)dx$

### Main topic:

Definite integrals

~ 0.08 seconds