不定积分，帮忙看下这道题？ 不定积分，求大佬帮忙看一下，这道题怎么写？
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绛旓細鍋涓嶅畾绉垎鐨棰樼洰鏃讹紝涓鑸渶瑕佸涓浜涘父瑙佺殑鍑芥暟鐨鍘熷嚱鏁銆佸鍑芥暟鐔熺粌鎺屾彙锛岃繖鏍锋墠鑳藉湪瑙ｉ鏃朵簨鍗婂姛鍊嶃
绛旓細1/[(ax + b)ⁿ(cx + d)] = A/(ax + b)ⁿ + B/(ax + b)ⁿ⁻¹ + ...+ X/(ax + b)² + Y/(ax + b) + Z/(cx + d)(ax + b)/[(cx² + dx + e)(fx + g)] = (Ax + B)/(cx² + dx + e) + C/(fx ...
绛旓細瑙ｅ涓嬪浘鎵绀
绛旓細鍏惰繃绋嬪彲浠ユ槸銆備护x+1/2=(鈭3/2)tan胃銆傗埓鍘熷紡=鈭玸ec胃d胃=鈭玸ec胃(sec胃+tan胃)d胃/(sec胃+tan胃)=鈭玠(sec胃+tan胃)/(sec胃+tan胃)=ln涓╯ec胃+tan胃涓+C銆傗埓鍘熷紡=ln涓2x+1+2鈭(x²+x+1涓+C=ln涓▁+1/2+鈭(x²+x+1涓+C銆備緵鍙傝冦
绛旓細1涓眰瀵煎嚭閿 3涓寲绠鍑洪敊 鍏蜂綋鐪嬪浘
绛旓細杩欎釜浠庤礋鏃犵┓鍒版鏃犵┓鐨绉垎涓1/鏍瑰彿2蟺銆傚鏋滄槸姹鍘熷嚱鏁鐨勮瘽鎶辨瓑锛屾棤娉曠敤鍒濈瓑鍑芥暟琛ㄧず銆傜洿鎺ヨ瀵熷彲寰椾粬鏄竴涓郴鏁颁箻浠ユ爣鍑嗘鎬佸垎甯冪殑瀵嗗害鍑芥暟锛岃瀵熻瀵熸爣鍑嗘鎬佺殑瀵嗗害灏卞彲浠ュ緱鍒1/鏍瑰彿2蟺锛屽洜涓轰换浣曟鐜囧瘑搴﹀嚱鏁扮殑绉垎閮芥槸1銆傜湡瑕佸仛鐨勮瘽涔熻兘鍋氥備护I绛変簬棰樼洰鐨勫井鍒嗐傝冭檻I鐨勫钩鏂广傚埄鐢ㄦ瀬鍧愭爣鐨勮浆鎹紝...
绛旓細浠=鈭(x-1)锛屽垯x=t^2+1锛宒x=2tdt 鍘熷紡=鈭玔(t^2+1)/t]*2tdt =2鈭(t^2+1)dt =(2/3)*t^3+2t+C =(2/3)*(x-1)^(3/2)+2鈭(x-1)+C锛屽叾涓瑿鏄换鎰忓父鏁
绛旓細1銆佺涓姝ュ氨閿欎簡锛屽簲鐢ㄤ笁瑙掑嚱鏁伴檷闃讹紝鍗硈in²伪=1/2锛1-cos2伪锛夈2銆佺劧鍚庡埄鐢ㄥ垎閮绉垎娉曟眰瑙ｃ3銆佹眰瑙ｈ繃绋嬪涓嬶細
绛旓細=鈭玜rctanxdx-鈭玿路arctanxdx =x路arctanx-鈭玿darctanx-½x²路arctanx+½鈭玿²darctanx =(x-½x²)arctanx-鈭玿dx/(1+x²)+½鈭玿²dx/(1+x²)=(x-½x²)arctanx-½鈭玠(1+x²)/(1+x²)...
绛旓細瑙ｏ細瀵硅绉嚱鏁拌繘琛屽垎姣嶆湁鐞嗗寲鏈夛紝鍘熷紡=鈭玔1+鈭(1-x^2)]^2dx/x^2=鈭玔2/x^2-1+2鈭(1-x^2)/x^2]dx锛屸埓鍘熷紡=-2/x-x-2鈭(1-x^2)/x-2鈭玠x/鈭(1-x^2)=(-2/x)[1+鈭(1-x^2)]-x-2arcsinx+C銆備緵鍙傝冦
