Determine the Integral by Making an Appropriate Substitution $\int x ^ { 2 } \sec ^ { 2 } x ^ { 3 }$

question 109

Multiple Choice

Determine the integral by making an appropriate substitution.
- $\int x ^ { 2 } \sec ^ { 2 } x ^ { 3 }$ dx

• A) tan \(x ^ { 3 }\) + C
• B) \(\tan ^ { 2 }\) \(x ^ { 3 }\) + C
• C) \(x ^ { 2 }\) sec \(x ^ { 3 }\) + C
• D) \(\frac { 1 } { 3 }\) tan \(x ^ { 3 }\) + C
• E) none of these

---

Definitions:

Seawater

The saltwater that makes up the oceans and seas, covering more than 70% of the Earth's surface.

Sediment

Particles of organic or inorganic matter that settle out of suspension in water, air, or ice, and accumulate in layers on the earth's surface.

Energetic Current

Refers to a strong, dynamic movement of water, often in the ocean, that can transport sediments and influence marine and coastal processes.

Moving

The act or process of changing location or position.