How to Calculate an Antiderivative

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When you begin your study of integral calculus, the first thing you will usually learn is the antiderivative. Simply stated, finding the antiderivative is the exact opposite process of finding the derivative of any given function. This means you must have a firm foundation in differential calculus before beginning a study of integral calculus. The process for finding the antiderivative for an algebraic equation is not very complex. You must either memorize or look up the antiderivative for some functions, such as logarithms and trigonometric functions.

  • Write the equation out so that all the exponents are visible. Remember that x^0 = 1, so include it along with any constant, as shown.

  • Add "1" to each exponent.

  • Divide each term by its new coefficient and simplify the exponents.

  • Add a constant to the equation to get the final answer. The derivative of this equation should equal the original equation, and the derivative of a constant is zero. This means that any arbitrary constant added to the antiderivative results in the same derivative. You must know some initial conditions for the function to determine the exact value of the constant or, if you do not have that information, you can usually just assume it is equal to zero.

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