The Integral of e^x: Calculating the Area Under the Curve with the Power Rule for Integration

int e^x

The expression “int e^x” represents the integral of the function e^x

The expression “int e^x” represents the integral of the function e^x. The integral is a fundamental concept in calculus that calculates the area under a curve.

To determine the integral of e^x, we use the power rule for integration, which states that the integral of x^n dx is (1/(n+1)) * x^(n+1) + C, where C is the constant of integration.

In the case of e^x, we have the function e^x raised to the power of 1, so n = 1. Applying the power rule, we find that the integral of e^x dx is (1/2) * e^x + C.

Therefore, the integral of e^x is (1/2) * e^x + C, where C is the constant of integration.

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