Comparing Integrals with Different Powers of Variable in the Denominator
<p>\( \int \frac{3}{x} dx \neq 3 \int \frac{1}{x} dx \)</p>
<p>Let's solve the integral on the left side:</p>
<p>\( \int \frac{3}{x} dx = 3 \int \frac{1}{x} dx \)</p>
<p>Since \( \int \frac{1}{x} dx = \ln|x| + C \), where C is the constant of integration, we have:</p>
<p>\( 3 \int \frac{1}{x} dx = 3(\ln|x| + C) = 3\ln|x| + C' \)</p>
<p>So, the equality given in the question is incorrect, because:</p>
<p>\( \int \frac{3}{x} dx = 3\ln|x| + C' \)</p>
<p>And not:</p>
<p>\( 3 \int \frac{1}{x} dx = 9\ln|x| + C' \)</p>
<p>There seems to be a misunderstanding or typo in the provided equality.</p>
