Here are the essential concepts you must grasp in order to answer the question correctly.
Partial Fraction Decomposition
Partial fraction decomposition breaks a rational function into simpler fractions that are easier to integrate. It is especially useful when the degree of the numerator is less than the degree of the denominator, allowing the integral to be expressed as a sum of simpler rational functions.
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Polynomial Division
Polynomial division is used when the degree of the numerator is equal to or greater than the degree of the denominator. It simplifies the integrand by dividing the polynomials, resulting in a polynomial plus a proper fraction, which can then be integrated using other techniques.
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Basic Integration Techniques
Basic integration techniques include recognizing standard integral forms and applying substitution or direct integration rules. After simplifying the integrand, these methods help evaluate the integral of polynomials, rational functions, or simpler expressions obtained from decomposition.
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