Evaluate the Integral $$\int x ^ { 2 } e ^ { x ^ { 3 } } d x$$

question 140

Multiple Choice

Evaluate the integral. The integral may not require integration by parts.
- $$\int x ^ { 2 } e ^ { x ^ { 3 } } d x$$

• A) \(\frac { 1 } { 3 } \mathrm { e } ^ { \mathrm { x } ^ { 3 } } + \mathrm { C }\)
• B) \(\frac { 1 } { 2 } e ^ { x ^ { 2 } } + C\)
• C) \(\frac { x ^ { 3 } } { 3 } e ^ { x ^ { 3 } } + C\)
• D) \(3 \mathrm { e } ^ { \mathrm { x } ^ { 3 } } + \mathrm { C }\)

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Definitions:

Hepatic Lobule

The functional unit of the liver, consisting of a hexagonal structure that processes nutrients, detoxifies harmful substances, and produces bile.

Portal Triad

A distinctive arrangement within the liver consisting of a bile duct, a branch of the hepatic artery, and a branch of the hepatic portal vein, essential for liver function.

Disaccharides

Sugars formed by the combination of two monosaccharides, such as sucrose and lactose.

Small Intestine

is the part of the gastrointestinal tract between the stomach and the large intestine, where most of the digestion and absorption of food takes place.