# Homework 5 Solution - Integration by Substitution SUGGESTED...

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Integration by SubstitutionSUGGESTED REFERENCE MATERIAL:As you work through the problems listed below, you should reference Chapter 5.3 of the rec-ommended textbook (or the equivalent chapter in your alternative textbook/online resource)and your lecture notes.EXPECTED SKILLS:Know how to simplify a “complicated integral” to a known form by making an appro-priate substitution of variables.PRACTICE PROBLEMS:For problems 1-21, evaluate the given indefinite integral and verify that youranswer is correct by differentiation.1.Z3x2(x3+ 3)3dx14(x3+ 3)4+C2.Z55x+ 3dxln|5x+ 3|+C3.Z2xcos (x2)dxsin (x2) +C4.Z4x(x2+ 6)2dx23(x2+ 6)3+C5.Zsec (4x) tan (4x)dx14sec (4x) +C6.Z(3x-5)9dx130(3x-5)10+C1
7.Ze-2xdx-12e-2x+C8.Zsinxcosx1 + sin2xdx12ln (1 + sin2x) +C9.Zcscx2cotx2dx-2 cscx2+C10.Z-3x31-x4dx12(1-x4)32+C11.Zexx-14cos 4xdx2ex-116sin (4x) +C12.Z12 + 4x2dx122arctan (2x) +C13.Z4x(3 +x2)2dx-2(3 +x2)-1+C14.Zx24-x dx.-323(4-x)3/2+165(4-x)5/2-27(4-x)7/2+C2
15.Z1q34+x-x2dx(HINT: Complete the square)arcsinx-12+C16.Ze3/xx2dx-13e3/x+C17.Zexe2x+ 1dxtan-1(ex) +C18.Z(sin 4x)(cos 4x)2/3dx-320(cos 4x)5/3+C19.Zcsc2(3x) tan
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