求不定积分 计算不定积分
\u6c42\u4e0d\u5b9a\u79ef\u5206\uff0c\u4e00\u5171\u4e09\u79cd\u65b9\u6cd51\u3001\u7b2c\u4e8c\u7c7b\u6362\u5143\u79ef\u5206\u6cd5
\u4ee4t=\u221a(x-1)\uff0c\u5219x=t^2+1\uff0cdx=2tdt
\u539f\u5f0f=\u222b(t^2+1)/t*2tdt
=2\u222b(t^2+1)dt
=(2/3)*t^3+2t+C
=(2/3)*(x-1)^(3/2)+2\u221a(x-1)+C\uff0c\u5176\u4e2dC\u662f\u4efb\u610f\u5e38\u6570
2\u3001\u7b2c\u4e00\u7c7b\u6362\u5143\u79ef\u5206\u6cd5
\u539f\u5f0f=\u222b(x-1+1)/\u221a(x-1)dx
=\u222b[\u221a(x-1)+1/\u221a(x-1)]d(x-1)
=(2/3)*(x-1)^(3/2)+2\u221a(x-1)+C\uff0c\u5176\u4e2dC\u662f\u4efb\u610f\u5e38\u6570
3\u3001\u5206\u90e8\u79ef\u5206\u6cd5
\u539f\u5f0f=\u222b2xd[\u221a(x-1)]
=2x\u221a(x-1)-\u222b2\u221a(x-1)dx
=2x\u221a(x-1)-(4/3)*(x-1)^(3/2)+C\uff0c\u5176\u4e2dC\u662f\u4f60\u4efb\u610f\u5e38\u6570
\u8ba1\u7b97\u4e0d\u5b9a\u79ef\u5206\uff0c\u9996\u5148\u8981\u628a\u63e1\u539f\u51fd\u6570\u4e0e\u4e0d\u5b9a\u79ef\u5206\u7684\u6982\u5ff5\uff0c\u57fa\u672c\u79ef\u5206\u6cd5\u53ea\u8981
\u719f\u8bb0\u5e38\u89c1\u4e0d\u5b9a\u79ef\u5206\u7684\u539f\u51fd\u6570\u5373\u53ef\u3002
\u6ce8\u610f\u628a\u63e1\u4e09\u79cd\u4e0d\u5b9a\u79ef\u5206\u7684\u8ba1\u7b97\u65b9\u6cd5\uff1a
\u76f4\u63a5\u79ef\u5206\u6cd5
2.\u6362\u5143\u79ef\u5206\u6cd5\uff08\u5176\u4e2d\u6709\u4e24\u79cd\u65b9\u6cd5\uff09
3.\u5206\u90e8\u79ef\u5206\u6cd5\u3002
下图提供三种积分方法的详细过程，点击放大，再点击再放大。
(图已经传上了，请稍等几分钟即可)
∫sec³xdx
=∫secxdtanx
=secxtanx-∫tanxdsecx
=secxtanx-∫secxtan²xdx
=secxtanx-∫secx(sec²x-1)dx
=secxtanx-∫sec³xdx+∫secxdx
=secxtanx-∫sec³xdx+ln|secx+tanx|
2∫sec³xdx=secxtanx+ln|secx+tanx|
∫sec³xdx=(secxtanx+ln|secx+tanx|)/2+C
∫sec3xdx
=∫secxdtanx
=secxtanx -∫tanxdsecx
=secxtanx-∫secxtan2xdx
=secxtanx-∫secx(sec2x-1)dx
=secxtanx-∫(sec3x-secx)dx
= secxtanx-∫sec3xdx-ln|secx+tanx|+C
所以∫sec3xdx=(secxtanx+ ln|secx+tanx|)/2+C
== 0.25 (sec x)^4 * (ln∣secx+tanx∣+C)
用复合函数求导法
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绛旓細浠=sint x锛0鈫1锛屽垯t锛0鈫捪/2 鈭玔0锛1]鈭(1-x²)dx =鈭玔0锛毾/2]鈭(1-sin²t)d(sint)=鈭玔0锛毾/2]cos²tdt =½鈭玔0锛毾/2](1+cos2t)dt =(½t+¼sin2t)|[0锛毾/2]=[½路(蟺/2)+¼sin蟺]-(½路0+¼...
