The antiderivative of e^(2x) can be found using the concept of integration. The function e^(2x) is an exponential function, and when integrating exponential functions, we typically apply the formula for the antiderivative of e^(kx), where k is a constant.
In this case, k = 2. The general formula for the antiderivative is:
∫ e^(kx) dx = (1/k)e^(kx) + C
So, applying this to our function:
∫ e^(2x) dx = (1/2)e^(2x) + C
Here, C represents the constant of integration, which accounts for any constant value that could have been present in the original function. Therefore, the antiderivative of e^(2x) is:
(1/2)e^(2x) + C
In conclusion, the antiderivative of e^(2x) is (1/2)e^(2x) + C. This result helps in calculus when dealing with problems related to area under curves and differential equations.