The formula of Integration by parts and the reduction formula

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How to set up the partial fraction in which the degree of polynomial in the numerator is less than or equal to the degree of the polynomial in the denominator. Also the formula of integration by parts and the reduction formula are explained with examples.
Prof. David Jerison, Single Variable Calculus: 27. Integration by Parts, Massachusetts Institute of Technology: MIT OpenCourseWare),http://ocw.mit.edu (Accessed July 23,2011). License: Creative Commons BY-NC-SA:http://ocw.mit.edu/terms/#cc

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