Example 1: Basic Integral of a Polynomial
Consider the integral ∫(2x3 + 3x2 - x + 4) dx. To solve this, we use the power rule for integration.
∫(2x3 + 3x2 - x + 4) dx = (1/2)x4 + x3 - (1/2)x2 + 4x + C
Where C is the constant of integration. Easy, right?
Example 2: Integral of an Exponential Function
Evaluate the integral ∫e2x dx. When the variable is an exponent, remember the base rule for exponential functions.
∫e2x dx = (1/2)e2x + C
Again, don't forget the constant of integration, C.