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輝念了崔遍匈 >> 〈sinx/(1+sin^2x)Dx=? >>

〈sinx/(1+sin^2x)Dx=?

〈sinx/(1+sin^2x)dx=-〈d(cosx)/[2-(cosx)^2] =-〈d(cosx)/─2+cosx─2-cosx =〈d(cosx)/─2+cosxcosx-〔2 =〔2/4〈[1/cosx-〔2-1/cosx+〔2]dcosx =〔2/4ln|(cosx-〔2)/(cosx+〔2)|+C

泌夕侭幣

1-sin2x=sin^2(x)+cos^2(x)-2sinxcosx=(sinx-cosx)^2 〈[〔1-sin2x) ]dx =〈|sinx-cosx|dx

泌夕侭幣

泌夕侭幣

e^x(sinx)^2=e^x[(1-cos2x)/2]=e^x/2-e^xcos2x/2.(e^xsin2x)'=2(cos2x)e^x+e^xsin2x(e^xcos2x)'=-2(sin2x)e^x+e^xcos2x.絞辛誼2(e^xsin2x)'+(e^xcos2x)'=5(cos2x)e^x.夸e^xcos2x/2=[2(e^xsin2x)'+(e^xcos2x)']/10

〈 (x + 2sinxcosx)/(1 + cos2x) dx = 〈 x/(1 + cos2x) dx + 〈 2sinxcosx/(1 + cos2x) dx = 〈 x/(1 + 2cos²x - 1) dx + 〈 sin2x/(1 + cos2x) dx = (1/2)〈 xsec²x dx - (1/2)〈 d(cos2x)/(1 + cos2x) = (1/2)〈 x d(tanx) - (1/2)〈 d(1 + ...

1-sin2x=(sinx-cosx)^2 〈(0,π/2)〔(1-sin2x)dx =〈(0,π/4)〔(1-sin2x)dx+〈(π/4,π/2)〔(1-sin2x)dx =〈(0,π/4)(cosx-sinx)dx+〈(π/4,π/2)(sinx-cosx)dx =(〔2-1)+(〔2-1) =2〔2-

B(1/2,1/4)=2〈(sinx)^(2*1/4-1)*(conx)^(2*1/2-1); B痕方p=1/2,q=1/4. B(1/2,1/4)=P(1/2)*P(1/4)/P(3/4);P,B痕方葎天性痕方。 P(1/2)=pi^1/2購噐P1/4珊嗤泣諒籾pi=3.1415926..... 総翌P(1/4)*P(3/4)=pi/sin1/4*pi B議持蛍袈律頁[0,pi/2]...

及匯籾及眉倖吉催頁委t算撹阻x遇sin(pi-x)=sin(x) ,cos^2(pi-x)=cos(x) 及屈籾圻云哘乎頁sin^2(-x)arctane^(-x)dx, 徽sin^2(-x)=sin^2(x) 甜痕方 侭參祥辛參委sin^2(-x)嶄議減催肇渠

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