What is the primitive of sinx/cos^2x? Homework Statement ∫e^(-x)(1-tanx)secx dx 2. Attempt at a solution I know ∫e^x(f(x)+f'(x))=e^x f(x) and I intuitively know f(x) could be secx here and therefore f'(x) will be secxtanx but I can't figure out how to reach ...
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.Evaluateexsinxdx Theformulafordefiniteintegrationbyparts (3)b a f (x)g(x)dx ...
(sin)^n (x) dx in terms of I (n-2) Let u = sinn-1 x du = (n-1)sinn-2 x cos x dx v = - cos x dv = sinx dx so integration by parts give: ∫〖sin〗^n x dx= -cos〖x 〖sin〗^(n-1) x+(n-1) ∫〖sin〗^(n-2) 〗 x cos^2〖x dx〗 Since cos2x =...
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 ...