Evaluate the Integral $$\int \mathrm { e } ^ { 2 x } \mathrm { x } ^ { 2 } \mathrm { dx }$$

question 31

Multiple Choice

Evaluate the integral.
- $$\int \mathrm { e } ^ { 2 x } \mathrm { x } ^ { 2 } \mathrm { dx }$$

• A) \(\frac { 1 } { 2 } x ^ { 2 } e ^ { 2 x } - \frac { 1 } { 4 } x e ^ { 2 x } + \frac { 1 } { 4 } e ^ { 2 x } + C\)
• B) \(\frac { 1 } { 2 } \mathrm { x } ^ { 2 } \mathrm { e } ^ { 2 \mathrm { x } } - \frac { 1 } { 2 } \mathrm { xe } ^{2 \mathrm { x } }+ \frac { 1 } { 4 } \mathrm { e } ^ { 2 \mathrm { x } } + \mathrm { C }\)
• C) \(\frac { 1 } { 2 } \mathrm { x } ^ { 2 } \mathrm { e } ^ { 2 \mathrm { x } } - \frac { 1 } { 2 } \mathrm { xe } ^ { 2 \mathrm { x } } + \mathrm { C }\)
• D) \(\frac { 1 } { 2 } x ^ { 2 } e ^ { 2 x } - x e ^ { 2 x } + \frac { 1 } { 4 } e ^ { 2 x } + C\)

---

Definitions:

HTML Document

A document written in HyperText Markup Language that defines the structure and layout of information on a webpage.

Query

A request for data or information from a database, typically expressed in a formal database query language.

HTML Tags

The codes used in HTML to create elements like headings, paragraphs, links, and images on web pages.

HTML Document

A file composed of Hypertext Markup Language code used to structure content and documents on the World Wide Web.