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MIT Integration Bee Qualifying Exam 23 January 2018

MIT Integration Bee Qualifying Exam23 January 20181 exex+ 2dx2 x 3 x 4 x 5 x dx3 2018 0|sin(2018x)|dx4 dxtanx+ cotx5 x52 +x12dx6 (cosxcoshx+ sinxsinhx)dx7 ex+ cosxex+ sinxdx8 sin(cos(sinx)) sin(sinx) cosx dx9 dx1 + sin(x)10 cosx1 cos(2x)dx11 ex(1/x+ logx)dx12 tanh2(x)dx13 2017x2016+ 2018x20171 +x4034+ 2x4035+x4036dx14 sin(2x) sin2xcos(2x) cos2xdx15 dxx2525 x1625+x92516 /20cos(x)2 cos2 (x)dx17 dx(1 +x2)3/218 dx x x x219 x 1x+x2logxdx20 csc(x) sec(x)dx

11 Z ex(1=x+logx)dx 12 Z tanh2(x)dx 13 Z 2017x2016 +2018x2017 1+x4034 +2x4035 +x4036 dx 14 Z sin(2x) sin2 x cos(2x) cos2 x dx 15 Z dx x25 25 x 16 25 +x 9 25 16 Z ˇ=2 0 cos(x) 2 2cos (x) dx 17 Z dx (1+x 2)3= 18 Z dx p

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  Cos 2x, Cos2

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Transcription of MIT Integration Bee Qualifying Exam 23 January 2018

1 MIT Integration Bee Qualifying Exam23 January 20181 exex+ 2dx2 x 3 x 4 x 5 x dx3 2018 0|sin(2018x)|dx4 dxtanx+ cotx5 x52 +x12dx6 (cosxcoshx+ sinxsinhx)dx7 ex+ cosxex+ sinxdx8 sin(cos(sinx)) sin(sinx) cosx dx9 dx1 + sin(x)10 cosx1 cos(2x)dx11 ex(1/x+ logx)dx12 tanh2(x)dx13 2017x2016+ 2018x20171 +x4034+ 2x4035+x4036dx14 sin(2x) sin2xcos(2x) cos2xdx15 dxx2525 x1625+x92516 /20cos(x)2 cos2 (x)dx17 dx(1 +x2)3/218 dx x x x219 x 1x+x2logxdx20 csc(x) sec(x)dx


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