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Evaluate the indefinite integral.$\int \frac{(\ln x)^{2}}{x} d x$
$\frac{(\ln x)^{3}}{3}+C$
Calculus 1 / AB
Calculus 2 / BC
Chapter 5
Integrals
Section 4
The Substitution Rule
Integration Techniques
Missouri State University
Harvey Mudd College
Idaho State University
Lectures
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this question asks us to evaluate the integral the integral natural log of X squared over x d x. The first step would be to break this up into natural log of X squared times one over X DX because now we can make Are you equivalent to natural log of X and then taking d'you? We have d'you the derivative of natural log of X is one axe. Therefore, we know we know have the integral of you square d u. We take the interval by increasing the exponents by one so increasing the expert from 2 to 3 dividing by the new exponents and then back substituting in are you is actually equivalent to natural of X So we have natural of x cubed divided by three plus c
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