不定积分换元上下限如何变 高等数学！ 求解！如图！ 定积分中 积分上下限是怎么变换 第...
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\u5982\u4eca\uff0cx-t=u
\u5f53t=0\u65f6\uff0cu=x
\u5f53t=x\u65f6\uff0cu=0
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1\u3001\u222b a dx = ax + C\uff0ca\u548cC\u90fd\u662f\u5e38\u6570
2\u3001\u222b x^a dx = [x^(a + 1)]/(a + 1) + C\uff0c\u5176\u4e2da\u4e3a\u5e38\u6570\u4e14 a \u2260 -1
3\u3001\u222b 1/x dx = ln|x| + C
4\u3001\u222b a^x dx = (1/lna)a^x + C\uff0c\u5176\u4e2da > 0 \u4e14 a \u2260 1
5\u3001\u222b e^x dx = e^x + C
6\u3001\u222b cosx dx = sinx + C
7\u3001\u222b sinx dx = - cosx + C
8\u3001\u222b cotx dx = ln|sinx| + C = - ln|cscx| + C
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\u5982\u4eca\uff0cx-t=u
\u5f53t=0\u65f6\uff0cu=x
\u5f53t=x\u65f6\uff0cu=0
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不定积分没有上下限吧。在积分好前加负号，定积分上下限交换。
根据x,y的取值范围画图，得到积分区域，再根据积分区域积分就可以了
绛旓細浠=tant锛宼鐨涓婁笅闄涓0鍒 娲/4 閭ｄ箞dx=(1/cost)^2dt锛1+x^2=1/(cost)^2 鎵浠^2 /(1+x^2)^3 =tant^2 *(cost)^6=(sint)^2 *(cost)^4 鍘绉垎=鈭 (sint)^2 *(cost)^2dt =鈭 1/4 (sin2t)^2 dt =鈭 1/8 -1/8 cos4t dt = t/8 -1/32 sin4t 浠ｅ叆t 鐨勪笂...
绛旓細鏂规硶濡備笅锛岃浣滃弬鑰冿細
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绛旓細鈭玞os²xdx=鈭½[1+cos(2x)]dx=鈭½dx+鈭½cos(2x)dx=鈭½dx+¼鈭玞os(2x)d(2x)=½x+¼sin(2x) +C
绛旓細璁緓=tant,dx=(sect)^2dt锛宻ect=鈭氾紙1+x^2),cost=1/鈭氾紙1+x^2)sint=x/鈭(1+x^2)鍘熷紡=鈭(sect)^2dt/[锛坱ant)^2*sect]=鈭(cost)^2sectdt/(sint)^2 =鈭玞ostdt/(sint)^2 =鈭玠(sint)/(sint)^2 =-1/sint+C =-[鈭氾紙1+x^2)]/x+C....
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