Question

Find the integral: \[ \int e^{3x} \, dx \]

• A. \( e^{3x} + k \)
• B. \( e^{x} + k \)
• C. \( e^{x^3} + k \)
• D. \( 3e^{3x} + k \)

Hint:

When integrating exponential functions, divide by the coefficient of \( x \) to apply the integration formula.

Answer 1

The Correct Option is C

We are asked to integrate \( e^{3x} \). The integral of \( e^{ax} \) is: \[ \int e^{ax} \, dx = \frac{e^{ax}}{a} + k. \] In our case, \( a = 3 \), so: \[ \int e^{3x} \, dx = \frac{e^{3x}}{3} + k. \] Thus, the correct answer is option (C) \( e^{3x} + k \).