Use Integration by Parts to Find the Indefinite Integral $\int x \cos 2 x d x$

question 3

Multiple Choice

Use integration by parts to find the indefinite integral. $\int x \cos 2 x d x$

• A) \(\frac { 1 } { 2 } x \cos 2 x - \frac { 1 } { 4 } \sin 2 x + C\)
• B) \(\frac { 1 } { 2 } x \sin 2 x - \frac { 1 } { 4 } \cos 2 x + C\)
• C) \(\frac { 1 } { 2 } \sin 2 x + \frac { 1 } { 2 } \cos 2 x + C\)
• D) \(\frac { 1 } { 2 } x \sin 2 x + \frac { 1 } { 4 } \cos 2 x + C\)
• E) \(\frac { 1 } { 4 } x \cos 2 x + \frac { 1 } { 2 } \sin 2 x + C\)

---

Definitions:

Muslin

A lightweight, finely woven cotton fabric used for making clothes, curtains, and other items.

Porous Paper

A type of paper designed to allow the passage of air and liquids through tiny holes or pores.

Sterile Areas

Locations, especially in medical settings, that are free from all forms of life, including microorganisms, to maintain asepsis.

Chemical Sterilization

A method of sterilization using chemical agents to eliminate all forms of life, including spores, from a surface or environment.