试题来源: 解析 【解析】(1 x_nx^x-e^x+c(2)-xcosx+sinx+c3 1/3x^3lnx-1/9x^3+c(4 -1/3xcos3x+1/9sin3x+c5 1/2xsin2x+1/4cos2x+c(6 xtanx+ln|cosx|+c(7 xlnx-x+c(8 x(lnx)^2-2xlnx+2x+c9 xarctanx-1/2ln(x^2+1)+c ...
Theformulaforintegrationbyparts (1)udvuvvdu Letu=f(x)andv=g(x)arebothdifferentiable,thendu=f’(x)dxanddv=g’(x)dx (2)f(x)g(x)dxf(x)g(x)f(x)g(x)dx Example1.Findxcosxdx Example2.Evaluatelnxdx Example3.Find x2exdx Example4....
integrate sec2 Solution:Iet’S “()一. :sec2ccz—xdtanz—mn—tanx一加nz一』 z —tanx+Jf—COS一2C。—t+ll。COSXl+ 酞帅plII:Tom托gratej 出· Solution:Choose “一 anddr= dex,thendu一 2xdx and 一 ex. So,integrationbypartscanbeusedasfollowing. e.r z 一 一 2『 :X2ex--2fxz(...
5、sinxdxdx(9)sincosxdxdx 2(10)sectanxdxdx2(11) csccotxdxdx 21(12)arcsin1dxdxx21(14)arctan1dxdxx21(13)arccos1dxdxx 21(15)arccot1dxdxx The Substitution Rulecxcuududxxxdxxu2sin21sin21cos2122cos212cos2xu2Example:Letthendxdu2ceceduedxxedxxexuuxuxx2222212121)2(212xu Letthenxdxdu2 The ...