Math Made Easy: Understanding the Antiderivative of e^x using the Power Rule

Antiderivative of e^x

The antiderivative of e^x is denoted as ∫ e^x dx

The antiderivative of e^x is denoted as ∫ e^x dx. To find this antiderivative, we can use the power rule of integration. In general, the power rule states that the antiderivative of x^n is (1 / (n+1)) * x^(n+1), where n is any real number except for -1.

In the case of e^x, we can think of it as e^1 * x^0, since e^1 = e and x^0 = 1. Applying the power rule, we find that the antiderivative of e^x is:

∫ e^x dx = e^x * (1 / 1) = e^x + C,

where C represents the constant of integration. Therefore, the antiderivative of e^x is simply e^x plus a constant.

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