# ∫ Log X 2 X D X - Mathematics

Sum
$\int\frac{\log x^2}{x} dx$

#### Solution

$\int\frac{\log x^2 dx}{x}$
$= \int\frac{2 \log x}{x} dx$
$= 2\int\frac{\log x}{x}dx$
$Let \log x = t$
$\Rightarrow \frac{1}{x} = \frac{dt}{dx}$
$\Rightarrow \frac{1}{x} dx = dt$
$Now, 2\int\frac{\log x}{x}dx$
$= 2\ ∫\text{ t dt}$
$= 2\left[ \frac{t^2}{2} \right] + C$
$= t^2 + C$
$= \left( \log x \right)^2 + C$

Concept: Definite Integral as the Limit of a Sum
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#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Exercise 19.9 | Q 28 | Page 58