The antiderivative of e^x is e^x itself. The antiderivative of a^x is a^x/ln a + C. Integration by parts is used when substitution method fails
The derivative of an indefinite integral equals the original function. For any function f(x), d/dx ∫ f(x) dx = f(x)
Derivative and antiderivative of exponential functions follow same three steps. Only difference is whether coefficient is multiplied or divided. Base 'a' determines growth/decay rate of exponential function
Indefinite integrals are found by integrating antiderivatives of integrals. Examples include finding integrals of x, 3ex, (3x² - 5x + 2)dx. Applications involve finding tangent slopes and population growth rates
Integration undoes differentiation by raising power to n+1 and adding constant. Integration with coefficients follows same formula as polynomials. Integration with variables requires multiplying out brackets and removing fractions
Integration means summing discrete data and finding functions from derivatives. Integration is opposite of differentiation and used for area calculations. Indefinite integration adds constant to represent uncalculated constant terms