Review Exercises –Integration Technique(for practice as needed –not to hand in)ComputeZf(x) dx for f(x) =1.13√3x2.x√2x2+ 13.x2x2+ 14.cos(x)3psin(x)5. ln(1 + x)6.e√x√x7. e√x8.1x3+ x9.1x3− x210.x2+ 1x2− 1(over for solutions)Integration Exercises – Answers1.Z13√3xdx =12(3x)23+ c . (Sub u = 3x or write integrand as 3−13· x13.)2.Zx√2x2+ 1dx =12√2x2+ 1 + c . (Sub u = 2x2+ 1; power rule w. p = −12.)3.Zx2x2+ 1dx =14ln(2x2+ 1) + c . (Sub u = 2x2+ 1; log rule.)4.Zcos(x)3psin(x)dx =32(sin(x))23+ c . (Sub u = sin x ; power rule with p = −13.)5.Zln(1 + x) dx = (x + 1) ln(x + 1) − x + c . (I. by parts: u = ln(1 + x) dv = 1.)6.Ze√x√xdx = 2 e√x+ c . (Sub u =√x ; exp rule.)7.Ze√xdx = 2 e√x(√x − 1) + c (Sub u =√x , then I. by parts.)8.Z1x3+ xdx = ln| x |√x2+ 1+ c. (P.F.’s with one quadratic factor.)9.Z1x3− x2dx = lnx − 1x+1x+ c. (P.F.’s.)10.Zx2+ 1x2− 1dx = x + lnx − 1x + 1+ c. (Long division &
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