integracion por partes, Diapositivas de Cálculo diferencial y integral

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INTEGRACIÓN POR FRACCIONES PARCIALES In this section we show how to integrate any rational function (a ratio of polynomials) by expressing it as a sum of simpler fractions, called partial fractions, that we already know how to integrate. To illustrate the method, observe that by taking the fractions 2/(x — 1) and 1/(x + 2) to a common denominator we obtain 2 1 2x + 2) — (lx — 1) x>+5 x=1 x>+2 (x — 1)(x + 2) Xxi+x-2 If we now reverse the procedure, we see how to integrate the function on the right side of this equation: +5 2 1 | = dw=| dx x+x-2 x=1. 1+2 =21In|x— 1| — In[lx+2|+ €