Question

\[ \int x^2 (x^4 + 1)^{3/4} \, dx \text{ is equal to } \]

• A. \( \left[ 1 + \frac{1}{x^4} \right]^{1/4} + C \)
• B. \( \left( x^4 + 1 \right)^{1/4} + C \)
• C. \( \left( 1 - \frac{1}{x^4} \right)^{1/4} + C \)
• D. \( \left( 1 + \frac{1}{x^4} \right)^{1/4} + C \)

Hint:

When integrating powers of binomials, use substitution to simplify the integrand and apply standard integration techniques.

Answer 1

The Correct Option is B

To solve the given integral, we use substitution and apply integration rules for powers of functions. The integral evaluates to \( \left( x^4 + 1 \right)^{1/4} + C \).
Step 2: Conclusion.
The correct answer is (B).