Question

Evaluate \[ \int \left( 27e^{9x} + e^{12x} \right)^{1/3} dx \]

• A. \( \frac{1}{4} (27e^{9x} + e^{3x})^3 + C \)
• B. \( \frac{1}{4} (27e^{9x} + e^{3x})^2 + C \)
• C. \( \frac{1}{3} (27e^{9x} + e^{3x})^4 + C \)
• D. \( \frac{1}{4} (27e^{9x} + e^{3x})^4 + C \)

Hint:

For integrals of complicated functions, use substitution to simplify and evaluate the integral.

Answer 1

The Correct Option is D

Using substitution and integration techniques, we simplify the integral and find the result as \( \frac{1}{4} (27e^{9x} + e^{3x})^4 + C \).
Final Answer: \[ \boxed{\frac{1}{4} (27e^{9x} + e^{3x})^4 + C} \]