Final answer:
Using partial fractions to find an indefinite integral involves decomposing a complex rational function into simpler fractions for easier integration, involving absolute values and adding the constant of integration, 'C'.
Step-by-step explanation:
The student's request for using partial fractions to find the indefinite integral involves a technique in calculus to break down complex rational functions into simpler fractions that can be more easily integrated. Assuming the question seeks an integral of the form ∫ (x^n) / (polynomial in x) dx, one would first verify that the degree of the numerator is less than the degree of the denominator, and if not, use polynomial division. Then, one would decompose the denominator into its linear and/or quadratic factors where possible and represent the original fraction as a sum of partial fractions, each corresponding to these factors. This allows for the integration of the terms separately, sometimes involving the use of absolute values when integrating terms that may result in logarithmic functions.
The step-by-step procedure often involves finding the values for the coefficients in the partial fraction representation by setting up equations based on the equality of the original fraction and the sum of partial fractions. Then, integral formulas or methods, such as integration by parts, are applied to integrate each of the partial fractions. Finally, all of the integrated terms are summed, and a constant of integration, typically denoted as 'C', is added.