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积分不确定度1.∫1(1

发布时间:2019-11-05     浏览次数:

赞美的反应
2007-07-0218:44:02
假设1,x = sinu
1(1-x ^ 2)/ x ^ 2 dx =∫(cotu)^ 2 du =∫[(cscu)^ 2-1]du = -cotu-u + C = - ((1-x ^ 2)/x弧标+ C
比方说2,x = asint
∫x^ 2((a ^ 2 - x ^ 2)dx = a ^ 4x∫(sintcost)^ 2 dt = a ^ 4/8 x(1 cos(4 t))dt = a ^ 4/8 x[t-1/4 x sin(4t)]+ C.
= a ^ 4/8 x[t-1/2 x sin(2t)x cos(2t)]+ C.
= a ^ 4/8×[t sint×cost×(1-2(sint)^ 2)]+ C.
= a ^ 4/8 x alkosine(x / a)-1 / 8 x x(a ^ 2-2 x ^ 2)((a ^ 2 x ^ 2)+ C
3,∫x^ 3 sinx dx
=-∫x^ 3d(cosx)
= -x ^ 3×cosx +3∫x^ 2 cos x dx
= -x ^ 3×cosx +3∫x^ 2d(sinx)
= -x ^ 3 x cosx + 3 x ^ 2 sinx-6 sin x sin x dx
= -x ^ 3×cos x + 3 x ^ 2 sinx +6∫xd(cos x)
= -x ^ 3 x cos x + 3 x ^ 2 sinx + 6 x cos x-6∫cosx dx
= -x ^ 3 x cos x + 3 x ^ 2 sinx + 6 x cos x-6 sinx + C.



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