[微積] 請問一題積分

[lineagenew (風華炎舞)]

想請問下面這題積分怎麼積呀？

解二階微方解到快出來的時候被這積分卡住了orz

∫1/(x^2+1)^2 dx

萬分感謝!!

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◆ From: 111.243.215.180
→ a88241050   :三角代換
→ t1552050027 :let x=tany
推 mvpnashmvp  :答案應該是arctanx+c
→ doublewhi   :它有個平方耶?  arctanx = =?
推 j0958322080 :S(cosx)^2 dx
推 goshfju     :x=tanθ -> 1+x^2=sec^2θ , dx=sec^2θdθ
→ lineagenew  :懂了!!! 感謝樓上諸位的提示~~^^
推 suhorng     :1/(1+x^2)^2 = 1/(1+x^2) - x^2/(1+x^2)
→ suhorng     :前者arctan, 後者分部積分：0.5x * 2x/(1+x^2)dx