Find the Integral Using an Appropriate Trigonometric Substitution $$\int \frac { x ^ { 3 } } { \sqrt { x ^ { 2 } + 1 } } d x$$

question 153

Multiple Choice

Find the integral using an appropriate trigonometric substitution. Select the correct answer.
$$\int \frac { x ^ { 3 } } { \sqrt { x ^ { 2 } + 1 } } d x$$

• A) \(\frac { 1 } { 3 } \left( x ^ { 2 } + 1 \right) ^ { 3 / 2 } \sqrt { x ^ { 2 } + 1 } + C\)
• B) \(\frac { 1 } { 3 } \left( x ^ { 2 } - 2 \right) \sqrt { x ^ { 2 } + 1 } + C\)
• C) \(\frac { 1 } { 3 } \left( x ^ { 2 } + 2 \right) \sqrt { x ^ { 2 } + 1 } + C\)
• D) \(\frac { 1 } { 3 } \left( x ^ { 2 } - 1 \right) ^ { 3 / 2 } \sqrt { x ^ { 2 } + 1 } + C\)

---

Definitions:

Outlet Stores

Retail stores that sell products directly from manufacturers at discounted prices, often offering overstocked items, seconds, or end-of-season goods.

Discount Retailers

Retail stores that offer products at lower prices than those of competitors, typically by selling items in bulk or with minimal services.

Supercenters

Large retail establishments that combine groceries and general merchandise goods under one roof, catering to a wide range of consumer needs.

Hypermarkets

Large retail spaces that combine a supermarket and a department store, offering a wide range of products under one roof.