高数，不定积分
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∫e^x*(1+sinx)/(1+cosx) dx，先拆开分子的括号
= ∫e^x/(1+cosx) dx + ∫(e^x)*sinx/(1+cosx) dx
= ∫e^x/(1+cosx) dx + ∫sinx/(1+cosx) de^x，将e^x积分后放进d里，进行分部积分法，第一个积分不变
= ∫e^x/(1+cosx) dx + e^x*sinx/(1+cosx) - ∫e^x d[sinx/(1+cosx)]，sinx/(1+cosx)和e^x互相调换了位置
= ∫e^x/(1+cosx) dx + e^x*sinx/(1+cosx) - ∫e^x * [cosx(1+cosx)-sinx(0-sinx)]/(1+cosx)² dx
= ∫e^x/(1+cosx) dx + e^x*sinx/(1+cosx) - ∫e^x * (cosx+cos²x+sin²x)/(1+cosx)² dx
= ∫e^x/(1+cosx) dx + e^x*sinx/(1+cosx) - ∫e^x * (1+cosx)/(1+cosx)² dx
= ∫e^x/(1+cosx) dx + e^x*sinx/(1+cosx) - ∫e^x/(1+cosx) dx，分子和分母约掉一个1+cosx
= e^x*sinx/(1+cosx) + C
= e^x*[2sin(x/2)cos(x/2)]/[1+2cos²(x/2)-1] + C，公式sin2x=2sinxcosx，cos2x=2cos²x-1
= (e^x)tan(x/2) + C
∫e^xdx/(1+cosx) +∫e^xsinxdx/(1+cosx)
=∫e^xd(x/2)/[cos(x/2)]^2 +∫tan(x/2)de^x
=∫e^xd(tan(x/2) +∫tan(x/2)de^x
=e^xtan(x/2)-∫tan(x/2)de^x+∫tan(x/2)de^x+C
=e^xtan(x/2)+C
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绛旓細鈭玣(x) dx = sinx/x +C f(x)= (xcosx -sinx)/x^2 // 鈭玿^3.f'(x) dx =鈭玿^3 df(x)=x^3 .f(x) -3鈭玿^2 .f(x) dx =x(xcosx -sinx) - 3鈭(xcosx -sinx) dx =x(xcosx -sinx) -3cosx - 3鈭玿cosx dx =x(xcosx -sinx) -3cosx - 3鈭玿dsinx =x(x...
绛旓細1-x^2)^(1/2)-2/3x+1/3arccosx*(1-x^2)^(3/2)-1/9x^3+C 2.sinxcosx/锛坰inx+cosx锛=sinxcosx/(2^1/2*sin(x+pi/4)),浠=pi/4+x,鍘熷紡鍖栫畝涓 1/(2*2^1/2)*(2(sinu)^2-1)/(sinu),鎵浠绉垎灏卞寲涓(1/2^1/2)*sinu-1/(2*2^1/2)*cscu.姹傝В鍗冲彲銆
