Question

Evaluate the integral: \[ \int e^{2x} \, dx \]

• A. \( e^{2x} + k \)
• B. \( \frac{x^2}{2} + k \)
• C. \( \frac{x^3}{3} + k \)
• D. \( 3x^3 + k \)

Hint:

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

Answer 1

The Correct Option is A

We are given the integral \( \int e^{2x} \, dx \). The integral of \( e^{ax} \) with respect to \( x \) is: \[ \int e^{ax} \, dx = \frac{e^{ax}}{a}. \] In our case, \( a = 2 \), so: \[ \int e^{2x} \, dx = \frac{e^{2x}}{2}. \] Thus, the correct answer is option (A).