What is the antiderivative of e^2x?

Solution:

The antiderivative is the integral of a function.

The integral of an exponential term e^ax is 1/a (e^ax)

On multiplying and dividing the function by 2, we get

⇒ ∫ e^2x = 1/2 ∫ 2e^2x dx

⇒ 1/2 ∫ e^2x d(2x)

Let u = 2x

⇒ 1/2 ∫ e^u du

⇒ 1/2 e^u

⇒ 1/2 e^2x

Thus, the antiderivative of e^2x is 1/2 e^2x

What is the antiderivative of e^2x?

Summary:

The antiderivative of e^2x is 1/2 e^2x