Lesson26_-_Integration_by_Substitution_ws-sol - Solutions...

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Solutions to Worksheet for Section 5.5Integration by SubstitutionV63.0121, Calculus ISpring 2010Find the following integrals.In the case of an indefinite integral, your answer should be themost general antiderivative. In the case of a definite integral, your answer should be a number.In these problems, a substitution is given.1.Z(3x-5)17dx,u= 3x-52.0
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Solution.We havedu=12xdx, which means thatZexxdx= 2Zeudu= 2eu+C4.Zcos 3x dx5 + 2 sin 3x,u= 5 + 2 sin 3xSolution.We havedu= 6 cos 3x dx, soZcos 3x dx5 + 2 sin 3x=16Zduu=16ln|u|+C=16ln|5 + 2 sin 3x|+CIn these problems, you need to determine the substitution yourself.5.Z(4-3x)7dx.

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