Indefinite Integration
Integration by Substitution
Grade 12
Question:
<p>Evaluate \(\int_3^5 x^5 \sqrt[3]{1 + 3x^4} \, dx\)</p>
<p>(A) \(\frac{5}{8}(1 + x^5)^{4/3}\sqrt[5]{6} + C\)</p>
<p>(B) \(\frac{5}{8}(1 + x^5)^{2/3}\sqrt[5]{6} + C\)</p>
<p>(C) \(\frac{5}{8}(1 + x^5)^{6/5}\sqrt[3]{4} + C\)</p>
<p>(D) None of these</p>
Step-by-Step Solution
Key Concept: Use substitution to transform the radical expression into a standard power form, then integrate.
<p>This is an indefinite integration problem requiring substitution and algebraic manipulation of the integrand.</p>
Correct Answer: B