2x的原函数是什么 cos^2X原函数是什么
e^2x\u7684\u539f\u51fd\u6570\u662f\u4ec0\u4e48\uff1fe^2x\u7684\u539f\u51fd\u6570\uff1a1/2e^2x+C\u3002C\u4e3a\u5e38\u6570\u3002
\u5206\u6790\u8fc7\u7a0b\u5982\u4e0b\uff1a
\u6c42e^2x\u7684\u539f\u51fd\u6570\uff0c\u5c31\u662f\u6c42e^2x\u7684\u4e0d\u5b9a\u79ef\u5206\u3002
\u222be^2xdx
=1/2\u222be^2xd2x
=1/2e^2x+C \uff08C\u4e3a\u5e38\u6570\uff09\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u5206\u90e8\u79ef\u5206\uff1a
(uv)'=u'v+uv'
\u5f97\uff1au'v=(uv)'-uv'
\u4e24\u8fb9\u79ef\u5206\u5f97\uff1a\u222b u'v dx=\u222b (uv)' dx - \u222b uv' dx
\u5373\uff1a\u222b u'v dx = uv - \u222b uv' d,\u8fd9\u5c31\u662f\u5206\u90e8\u79ef\u5206\u516c\u5f0f
\u4e5f\u53ef\u7b80\u5199\u4e3a\uff1a\u222b v du = uv - \u222b u dv
\u5e38\u7528\u79ef\u5206\u516c\u5f0f\uff1a
1\uff09\u222b0dx=c
2\uff09\u222bx^udx=(x^(u+1))/(u+1)+c
3\uff09\u222b1/xdx=ln|x|+c
4\uff09\u222ba^xdx=(a^x)/lna+c
5\uff09\u222be^xdx=e^x+c
6\uff09\u222bsinxdx=-cosx+c
7\uff09\u222bcosxdx=sinx+c
8\uff09\u222b1/(cosx)^2dx=tanx+c
9\uff09\u222b1/(sinx)^2dx=-cotx+c
10\uff09\u222b1/\u221a\uff081-x^2) dx=arcsinx+c
cos^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
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2x的原函数为x²+C
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