不定积分题目有哪位大佬帮忙算一下吗？根号（1-x^2）/x 不定积分根号下(1-x^2)/x
\u4e0d\u5b9a\u79ef\u5206\u9898\u76ee\u6709\u54ea\u4f4d\u5927\u4f6c\u5e2e\u6211\u7b97\u4e00\u4e0b\u5417\uff1f\u6839\u53f7\uff082-x^2\uff09\u4ee4x=atanu\uff0c\u5219u=arctan(x/a)
\u222b[1/\u221a(x²+a²)]dx
=\u222b[1/\u221a(a²tan²u+a²)]d(atanu)
=\u222bcosu\u00b7sec²udu
=\u222bsecudu
=ln|secu+tanu| +C
=ln|\u221a(x²+a²)/a +x/a| +C
=ln|[\u221a(x²+a²)+x]/a| +C
\u4ee4\u221a\uff081\uff0dx^2\uff09\uff1du\uff0c\u52191\uff0dx^2\uff1du^2\uff0c\u2234x^2\uff1d1\uff0du^2\uff0c\u2234d\uff08x^2\uff09\uff1d\uff0d2udu\u3002
\u2234\u222b\uff3b\u221a\uff081\uff0dx^2\uff09/x\uff3ddx
\uff1d\uff081/2\uff09\u222b\uff3b\u221a\uff081\uff0dx^2\uff09/x^2\uff3dd\uff08x^2\uff09
\uff1d\uff081/2\uff09\u222b\uff3bu/\uff081\uff0du^2\uff09\uff3d\uff08\uff0d2u\uff09du
\uff1d\u222b\uff3bu^2/\uff08u^2\uff0d1\uff09\uff3ddu
\uff1d\u222b\uff3b\uff08u^2\uff0d1\uff0b1\uff09/\uff08u^2\uff0d1\uff09\uff3ddu
\uff1d\u222b\uff3b1\uff0b1/\uff08u^2\uff0d1\uff09\uff3ddu
\uff1d\u222bdu\uff0b\u222b\uff3b1/\uff08u^2\uff0d1\uff09\uff3ddu
\uff1du\uff0b\uff081/2\uff09\u222b\uff3b\uff08u\uff0b1\uff0du\uff0b1\uff09/\uff08u^2\uff0d1\uff09\uff3ddu
\uff1d\u221a\uff081\uff0dx^2\uff09\uff0b\uff081/2\uff09\u222b\uff3b1/\uff08u\uff0d1\uff09\uff3ddu\uff0d\uff081/2\uff09\u222b\uff3b1/\uff08u\uff0b1\uff09\uff3ddu
\uff1d\u221a\uff081\uff0dx^2\uff09\uff0b\uff081/2\uff09ln\uff5cu\uff0d1\uff5c\uff0d\uff081/2\uff09ln\uff5cu\uff0b1\uff5c\uff0bC
\uff1d\u221a\uff081\uff0dx^2\uff09\uff0b\uff081/2\uff09ln\uff5c\u221a\uff081\uff0dx^2\uff09\uff0d1\uff5c\uff0d\uff081/2\uff09ln\uff5c\u221a\uff081\uff0dx^2\uff09\uff0b1\uff5c\uff0bC\u3002
\uff1d\u221a\uff081\uff0dx^2\uff09\uff0b\uff081/2\uff09ln\uff5c\uff3b\u221a\uff081\uff0dx^2\uff09\uff0d1\uff3d/\uff3b\u221a\uff081\uff0dx^2\uff09\uff0b1\uff3d\uff5c\uff0bC
\uff1d\u221a\uff081\uff0dx^2\uff09\uff0b\uff081/2\uff09ln\uff5c\uff3b1\uff0d\u221a\uff081\uff0dx^2\uff09\uff3d/\uff3b1\uff0b\u221a\uff081\uff0dx^2\uff09\uff3d\uff5c\uff0bC
\uff1d\u221a\uff081\uff0dx^2\uff09\uff0b\uff081/2\uff09ln\uff5c\uff3b1\uff0d\u221a\uff081\uff0dx^2\uff09\uff3d^2/\uff3b1\uff0d\uff081\uff0dx^2\uff09\uff3d\uff5c\uff0bC
\uff1d\u221a\uff081\uff0dx^2\uff09\uff0b\uff081/2\uff09ln\uff5c\uff3b1\uff0d\u221a\uff081\uff0dx^2\uff09\uff3d/x\uff5c^2\uff0bC
\uff1d\u221a\uff081\uff0dx^2\uff09\uff0bln\uff5c\uff3b1\uff0d\u221a\uff081\uff0dx^2\uff09\uff3d/x\uff5c\uff0bC
你好，这个题目使用三角换元法，具体解题过程如下图
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