# ∫ X Sin 2 X D X - Mathematics

Sum
$\int x \text{ sin 2x dx }$

#### Solution

$\int x \text{ sin 2x dx }$
 "Taking x as the first function and sin 2x as the second function  " .
$= x\int\text{ sin 2x dx} - \int\left\{ \frac{d}{dx}\left( x \right)\int\text{ sin 2x dx }\right\}dx$
$= \frac{- x \cos 2x}{2} + \int\frac{\cos 2x}{2}dx$
$= \frac{- x \cos 2x}{2} + \frac{\sin 2x}{4} + C$

Concept: Indefinite Integral Problems
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#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Exercise 19.25 | Q 9 | Page 133