cos^2x/sin^2x的原函数是什么?
cos^2X\u539f\u51fd\u6570\u662f\u4ec0\u4e48cos^2x\u7684\u539f\u51fd\u6570\u4e3a1/2x+1/4sin2x+C
\u89e3\uff1a\u4ee4F(x)\u4e3acos^2x\u7684\u539f\u51fd\u6570\u3002\u90a3\u4e48
F(x)=\u222bcos^2xdx
=\u222b(cos2x+1)/2dx
=1/2\u222bcos2xdx+1/2\u222b1dx
=1/4\u222bcos2xd(2x)+1/2\u222b1dx
=1/2x+1/4sin2x+C
\u6269\u5c55\u8d44\u6599\uff1a
1\u3001\u4e09\u89d2\u51fd\u6570\u57fa\u672c\u516c\u5f0f
\uff081\uff09\u4e09\u89d2\u51fd\u6570\u4e4b\u95f4\u53d8\u6362
tanx=sinx/cosx\u3001cotx=cosx/sinx\u3001secx=1/cosx\u3001cscx=1/sinx\u3001
tanx*cotx=1\u30011=(sinx)^2+(cosx)^2\u3002
\uff082\uff09\u4e8c\u500d\u89d2\u516c\u5f0f
cos2x=2cos²x-1=1-2sin²x\u3001cos²x=(cos2x+1)/2\u3001sin²x=(1-c0s2x)/2
2\u3001\u79ef\u5206\u516c\u5f0f\u6cd5\u6c42\u89e3\u4e0d\u5b9a\u79ef\u5206
\u76f4\u63a5\u5229\u7528\u79ef\u5206\u516c\u5f0f\u6c42\u51fa\u4e0d\u5b9a\u79ef\u5206\u3002
\u4f8b\uff1a\u222be^xdx=e^x\u3001\u222b1/xdx=ln|x|+C\u3001\u222bcosxdx=sinx+C\u3001\u222bsinxdx=-cosx+C
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u4e0d\u5b9a\u79ef\u5206
\uff08sin\u22274xcos\u22272x\uff09\u7684\u539f\u51fd\u6570\u662f
\u222b\uff08sin\u22274xcos\u22272x\uff09dx
=\u222b[sin^2x(sinxcosx)^2dx
=1/8\u222b(1-cos2x)(sin2x)^2dx
=1/8\u222b(sin2x)^2dx-1/16\u222b(sin2x)^2d(sin2x)
=1/16\u222b[1-cos4x]dx-1/48(sin2x)^3
=x/16-1/64*sin4x-1/48*(sin2x)^3+C
\u539f\u51fd\u6570\u7684\u5b9a\u4e49
primitive function\u5df2\u77e5\u51fd\u6570f(x)\u662f\u4e00\u4e2a\u5b9a\u4e49\u5728\u67d0\u533a\u95f4\u7684\u51fd\u6570\uff0c\u5982\u679c\u5b58\u5728\u53ef\u5bfc\u51fd\u6570F(x)\uff0c\u4f7f\u5f97\u5728\u8be5\u533a\u95f4\u5185\u7684\u4efb\u4e00\u70b9\u90fd\u6709
dF(x)=f(x)dx\uff0c
\u5219\u5728\u8be5\u533a\u95f4\u5185\u5c31\u79f0\u51fd\u6570F(x)\u4e3a\u51fd\u6570f(x)\u7684\u539f\u51fd\u6570\u3002
\u4f8b\uff1asinx\u662fcosx\u7684\u539f\u51fd\u6570\u3002
\u51e0\u4f55\u610f\u4e49\u548c\u529b\u5b66\u610f\u4e49
\u8bbef(x)\u5728[a,b]\u4e0a\u8fde\u7eed\uff0c\u5219\u7531\u66f2\u7ebfy=f(x),x\u8f74\u53ca\u76f4\u7ebfx=a,x=b\u56f4\u6210\u7684\u66f2\u8fb9\u68af\u5f62\u7684\u9762\u79ef\u51fd\u6570(\u6307\u4ee3\u6570\u548c\u2014\u2014x\u8f74\u4e0a\u65b9\u53d6\u6b63\u53f7\uff0c\u4e0b\u65b9\u53d6\u8d1f\u53f7)\u662ff(x)\u7684\u4e00\u4e2a\u539f\u51fd\u6570\u00b7\u82e5x\u4e3a\u65f6\u95f4\u53d8\u91cf\uff0cf(x)\u4e3a\u76f4\u7ebf\u8fd0\u52a8\u7684\u7269\u4f53\u7684\u901f\u5ea6\u51fd\u6570\uff0c\u5219f(x)\u7684\u539f\u51fd\u6570\u5c31\u662f\u4f4d\u79fb\u51fd\u6570\u00b7
=∫(csc²-1)dx
=-cotx-x+C
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