joe foster u substitution recall the substitution rule from math 141 see page 241 in the textbook theorem if u g x is a dierentiable function whose range is an ...
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...Joe foster u substitution recall the rule from math see page in textbook theorem if g x is a dierentiable function whose range an interval i and f continuous on then dx du this method of integration helpful reversing chain can you why let s look at some examples example find sec tan c remember for indenite integrals your answer should be terms same variable as start with so to substitute back evaluate integral hi above we changed limits coincide our doing means that don t have end like but did use original worry get try it yourself now p sin illustrates there may not immediately obvious cases fractions poly nomials power numerator had degree was zero make successful would need polynomial obviously denominator forced appear by completing square rst practice problems below stuck are hints next do without looking them chances won exam cos e dt exsin ex xdx xcos ln csc cot d xe xsin challenge harder require little more thinking algebraic manipulation substitutions work...