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Unformatted text preview: (c) y = ln5−3x 2  Derivative of lnu is u'/u where u is the value value u = 5−3x 2 u’ = −6x f’(x) = The process: Change the integral given in terms of x ( ) to an equivalent, simpler integral in terms of u ( ) 2. Integrals requiring usubstitution The plan is to replace the part of an integral that makes it impossible to get the integral. The complicated part is replaced with u and a new, simpler integral is made. Then get the antiderivative F(u) … this is in terms of u Convert F(u) back to terms of x so the integral is F(x) + C 3. u can substitute for different parts Integrate each. (d) (e) (f) Ex( Let u be inside ( )’ s ) — Integrate each. (g) (h) What is wrong with this problem such that it cannot be done using usubstitution? Ex( Let u be exponent of e u ) — Integrate each. (i) (j) Ex( Let u be the dominator of 1/u ) — Integrate each. (k) (j) Ex( Let u be lnx ) —...
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This note was uploaded on 02/21/2011 for the course MATH 408C taught by Professor Knopf during the Spring '10 term at University of Texas.
 Spring '10
 KNOPF
 Chain Rule, Derivative

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