求不定积分∫arccosx/(√1-x^2)dx 求arccosx/√(1+x2)的不定积分，谢谢！
\u6c42\u4e0d\u5b9a\u79ef\u520610^arccosx/\u221a1-x²dx\u222b10^arccosx/\u221a1-x²dx
=- \u222b10^arccosxdarccosx
= -10^arccosx/ln10 + C
\u4e00\u4e2a\u51fd\u6570\uff0c\u53ef\u4ee5\u5b58\u5728\u4e0d\u5b9a\u79ef\u5206\uff0c\u800c\u4e0d\u5b58\u5728\u5b9a\u79ef\u5206\uff0c\u4e5f\u53ef\u4ee5\u5b58\u5728\u5b9a\u79ef\u5206\uff0c\u800c\u6ca1\u6709\u4e0d\u5b9a\u79ef\u5206\u3002\u8fde\u7eed\u51fd\u6570\uff0c\u4e00\u5b9a\u5b58\u5728\u5b9a\u79ef\u5206\u548c\u4e0d\u5b9a\u79ef\u5206\u3002
\u82e5\u5728\u6709\u9650\u533a\u95f4[a\uff0cb]\u4e0a\u53ea\u6709\u6709\u9650\u4e2a\u95f4\u65ad\u70b9\u4e14\u51fd\u6570\u6709\u754c\uff0c\u5219\u5b9a\u79ef\u5206\u5b58\u5728\uff1b\u82e5\u6709\u8df3\u8dc3\u3001\u53ef\u53bb\u3001\u65e0\u7a77\u95f4\u65ad\u70b9\uff0c\u5219\u539f\u51fd\u6570\u4e00\u5b9a\u4e0d\u5b58\u5728\uff0c\u5373\u4e0d\u5b9a\u79ef\u5206\u4e00\u5b9a\u4e0d\u5b58\u5728\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u6c42\u51fd\u6570f(x)\u7684\u4e0d\u5b9a\u79ef\u5206\uff0c\u5c31\u662f\u8981\u6c42\u51faf(x)\u7684\u6240\u6709\u7684\u539f\u51fd\u6570\uff0c\u7531\u539f\u51fd\u6570\u7684\u6027\u8d28\u53ef\u77e5\uff0c\u53ea\u8981\u6c42\u51fa\u51fd\u6570f(x)\u7684\u4e00\u4e2a\u539f\u51fd\u6570\uff0c\u518d\u52a0\u4e0a\u4efb\u610f\u7684\u5e38\u6570C\u5c31\u5f97\u5230\u51fd\u6570f(x)\u7684\u4e0d\u5b9a\u79ef\u5206\u3002
\u628a\u51fd\u6570\u5728\u67d0\u4e2a\u533a\u95f4\u4e0a\u7684\u56fe\u8c61[a\uff0cb]\u5206\u6210n\u4efd\uff0c\u7528\u5e73\u884c\u4e8ey\u8f74\u7684\u76f4\u7ebf\u628a\u5176\u5206\u5272\u6210\u65e0\u6570\u4e2a\u77e9\u5f62\uff0c\u518d\u6c42\u5f53n\u2192+\u221e\u65f6\u6240\u6709\u8fd9\u4e9b\u77e9\u5f62\u9762\u79ef\u7684\u548c\u3002
\u628a\u76f4\u89d2\u5750\u6807\u7cfb\u4e0a\u7684\u51fd\u6570\u7684\u56fe\u8c61\u7528\u5e73\u884c\u4e8ey\u8f74\u7684\u76f4\u7ebf\u628a\u5176\u5206\u5272\u6210\u65e0\u6570\u4e2a\u77e9\u5f62\uff0c\u7136\u540e\u628a\u67d0\u4e2a\u533a\u95f4[a\uff0cb]\u4e0a\u7684\u77e9\u5f62\u7d2f\u52a0\u8d77\u6765\uff0c\u6240\u5f97\u5230\u7684\u5c31\u662f\u8fd9\u4e2a\u51fd\u6570\u7684\u56fe\u8c61\u5728\u533a\u95f4[a\uff0cb]\u7684\u9762\u79ef\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1--\u4e0d\u5b9a\u79ef\u5206
\u662f(arccosx)/\u221a(1+x^2)\u4e48\uff1f\uff1f\u8fd9\u4e2a\u597d\u50cf\u6c42\u4e0d\u51fa\u539f\u51fd\u6570\u7684\uff0c\u91cc\u8fb9\u6709\u4e2aLi\u51fd\u6570\uff0c\u4e0d\u662f\u521d\u7b49\u51fd\u6570\u3002
\u8fd9\u4e2aarccos[x/\u221a(1+x^2)]\u53ef\u4ee5\u6c42\u51fa\u539f\u51fd\u6570\u7684\u3002\u8fd9\u4e2a\u7528\u5206\u90e8\u79ef\u5206\u6c42\uff0c
\u222barccos[x/\u221a(1+x^2)]dx
=xarccos[x/\u221a(1+x^2)]-\u222bx darccos[x/\u221a(1+x^2)]
=xarccos[x/\u221a(1+x^2)]- \u222b[x/(1+x^2)]dx
=xarccos[x/\u221a(1+x^2)]-(1/2)\u222bd(x^2)/(1+x^2)
=xarccos[x/\u221a(1+x^2)]-ln\u221a(1+x^2)+C
=-∫arccosxdarccosx
=-1/2(arccosx)^2 + C
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