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摘要： 试求：\(\int \sqrt{1-x^2}dx\) \[ \int \sqrt{1-x^2}dx \xlongequal[p^2+x^2=1]{p=\sqrt{1-x^2}}\int pdx \] 则 \(pdp+xdx=0\)，再考虑 \(I=\int pdx,J=\int xdp\)，则： \ 阅读全文

摘要： 试求：\(\int \frac{dx}{(1+x^2)^2}\) \[ \begin{aligned} \int \frac{dx}{(1+x^2)^2} =& \int \frac{\sec^2t dt}{\sec^4t} \\ =&\int \cos^2 t dt \\ =&\frac{1}{4 阅读全文