1／2－tanx^2的不定积分怎么算 1／2+tanx^2的不定积分是什么算，用换元
1\uff0f\uff082\uff0dtanx^2\uff09\u7684\u4e0d\u5b9a\u79ef\u5206\u89e3\uff1a\u8bbet=tanx\uff0c\u2234dx=dt/(1+t²)\u3002
\u2234\u539f\u5f0f=\u222bdt/[(2-t²)(1+t²)]=(1/3)\u222bdt/[1/(1+t²)+1/(2-t²)]=(1/3)arctant+(1/3)\u222bdt/(2-t²)\u3002
\u800c\uff0c\u222bdt/(2-t²)=[1/(2\u221a2)]\u222b[1/(\u221a2-t)+1/(\u221a2+t)]dt=[1/(2\u221a2)]ln\u4e28(\u221a2+t)/(\u221a2-t)\u4e28+C1,\u3002
\u2234\u539f\u5f0f=(1/3)arctan(tanx)+[1/(6\u221a2)]]ln\u4e28(\u221a2+tanx)/(\u221a2-tanx)\u4e28+C\u3002
\u4f9b\u53c2\u8003\u3002
(tanx)^2=(secx)^2-1\uff0c\u6240\u4ee5(tanx)^2\u7684\u4e0d\u5b9a\u79ef\u5206\u5373\u4e3atanx-x+C\uff08\u7b54\u9898\u4e0d\u5bb9\u6613\uff0c\u8bda\u5fc3\u4e3a\u4f60\u89e3\u7b54\uff0c\u7ed9\u4e2a\u597d\u8bc4\u5427\uff01\u8c22\u8c22\u5566\uff01\uff01\uff01\uff09
1／2-∫(tanx)^2dx=1/2-∫[(secx)^2-1]dx
=1/2-(∫(secx)^2dx-x)
=1/2-tanx+x-C
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绛旓細璁＄畻锛tanx锛²涓嶅畾绉垎鐨勬柟娉曪細锛坱anx锛²=鈭玔(secx)^2-1]dx =鈭(secx)^2dx-x =tanx-x+c
绛旓細1/tan^2x鐨勫師鍑芥暟绛変簬cotx-x+C锛孋涓哄父鏁般傝В锛氫护f(x)=1/(tanx)^2锛孎(x)涓篺(x)鐨勫師鍑芥暟銆傞偅涔團(x)=鈭玣(x)dx=鈭1/(tanx)^2dx=鈭(cosx)^2/(sinx)^2dx=鈭(1-(sinx)^2)/(sinx)^2dx=鈭1/(sinx)^2dx-鈭1dx=cotx-x+C锛孋涓哄父鏁般傚嵆1/tan^2x鐨勫師鍑芥暟绛変簬cotx-x+C锛孋涓...
绛旓細(1)鈭玹an锛2 xdx 锛=鈭(sec²x-1)dx =tanx-x+c (2).鈭玠x/(1-2x)锛(1/2)=-1/2 鈭1/(1-2x)锛(1/2) d(1-2x)=-(1-2x)^(1/2)+c
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绛旓細鈭(tanx)^2dx=鈭紙sinx)^2/(cosx)^2dx=鈭玔1-(cosx)^2]/(cosx)^2dx=鈭1/(cosx)^2dx-鈭玠x=tanx-x+C 姹傚嚱鏁癴(x)鐨勪笉瀹氱Н鍒锛屽氨鏄姹傚嚭f(x)鐨勬墍鏈鐨勫師鍑芥暟锛岀敱鍘熷嚱鏁扮殑鎬ц川鍙煡锛屽彧瑕佹眰鍑哄嚱鏁癴(x)鐨勪竴涓師鍑芥暟锛屽啀鍔犱笂浠绘剰鐨勫父鏁癈灏卞緱鍒板嚱鏁癴(x)鐨勪笉瀹氱Н鍒嗐傝鍑芥暟鍜寀锛寁鍏锋湁...
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