## Problem Statement

Calculate the indefinite integral:

$$
\int \frac{1+\ln x}{x} d x
$$
## Solution

## Method 1

$$
\int \frac{1+\ln x}{x} d x=\int(1+\ln x) d(\ln x)=\ln x+\frac{1}{2} \ln ^{2} x+C
$$

## Method 2

$$
\int \frac{1+\ln x}{x} d x=\int \frac{d x}{x}+\int \frac{\ln x d x}{x} d x=\ln |x|+\int \ln x d(\ln x)=\ln |x|+\frac{1}{2} \ln ^{2} x+C
$$

Source — "http://pluspi.org/wiki/index.php/\�\�\�\�\�\�\�\�\�\�\�\� \%D0\%9A\%D1\%83\%D0\%B7\%D0\%BD\%D0\%B5\%D1\%86\%D0\%BE\%D0\%B2_\%D0\%98\%D0\%BD $\% \mathrm{D} 1 \% 82 \% \mathrm{D} 0 \% \mathrm{~B} 5 \% \mathrm{D} 0 \% \mathrm{~B} 3 \% \mathrm{D} 1 \% 80 \% \mathrm{D} 0 \% \mathrm{~B} 0 \% \mathrm{D} 0 \% \mathrm{BB} \% \mathrm{D} 1 \% 8 \mathrm{~B}+3-2$ "

Categories: Kuznetsov's Problem Book Integrals Problem 3 | Integrals

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## Problem Kuznetsov Integrals 3-3

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