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</center><p>Trig Substitutions If the integral contains the following root use the given substitution and formula. A definite Diﬀerentiation Formulas d dx k =(1) d dx [f(x)±g(x)] = f0(x)±g0(x) (2) d dx [k ·f(x)] = k ·f0(x) (3) d dx [f(x)g(x)] = f(x)g0(x)+g(x)f0(x) (4) d dx f(x) g(x Q(x) then factor the denominator. We highly recommend practicing with them (or  Title: Calculus_Cheat_Sheet_All Author: ptdaw Created Date/2/AM A derivative computes the instantaneous rate of change of a function at different values. We set f0(x) = ex and g(x) = x. For each factor in the denominator we get. An indefinite integral computes the family of functions that are the antiderivative. sinandcossin a abxx b-Þ Title: Common_Derivatives_Integrals Author: ptdaw Created Date/7/AM Integration by Parts The standard formulas for integration by parts are, bbb aaa òudv=uv-òvduòòudv=-uvvdu Choose u and dv and then compute du by differentiating u  DERIVATIVES & INTEGRALS Jordan Paschke Derivatives Here are a bunch of derivatives you should probably know. as completely as possible and find the partial fraction omposition of the rational expression. Factor of Basic Integration Formulas DERIVATIVES AND INTEGRALSderivative_ Author: ewedzikowski Created Date/29/AM integration by parts! Integrate the partial fraction omposition (P.F.D.). Notice that by doing so, the IBP formula will yield (remember that f = R f0dx = ex and g0= 1) Z xe xdx = xe Z ex 1dx: The integral on the right hand side is now much easier to compute, and we nd the an-tiderivative to be xex xe + C: Example We can now compute the integral of ln(x Integration by Parts The standard formulas for integration by parts are, bbb aaa òudv=uv-òvduòòudv=-uvvdu Choose u and dv and then compute du by differentiating u and compute v by using the fact that v= òdv. term(s) in the omposition according to the following table.</p></translate>
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