求x∧2e∧x∧3dx的不定积分 求不定积分∫x∧2e∧(-x∧3)dx
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绛旓細2015-01-02 姹備笅鍒椾笉瀹氱Н鍒,鈭x鈭2e鈭dx 1 2016-12-11 (x+1)鈭2/(x鈭2+1)鈭2鐨勪笉瀹氱Н鍒 2015-12-01 姹倄鈭3/x+3鐨勪笉瀹氱Н鍒,甯屾湜姝ラ鑳借缁 7 2015-04-03 姹倄/(1+x鈭2)鐨勪笉瀹氱Н鍒 3 2012-02-20 鈭(1+2e^x)/(2e^x+x)dx鐨勪笉瀹氱Н鍒嗘庝箞姹 4 鏇村绫讳技闂 > 涓轰綘鎺ㄨ崘: ...
绛旓細=(1/5)鈭(lnx)^2dx^a11锛屼互涓嬬涓娆′娇鐢ㄥ垎閮ㄧН鍒嗘硶锛=(1/5) (lnx)^2*x^5-(1/5)鈭玿^5d(lnx)^2 =(1/5) (lnx)^2*x^5-(2/5)鈭玿^5*lnx*(1/x)dx =(1/5) (lnx)^2*x^5-(2/5)鈭玿^4*lnxdx =(1/5) (lnx)^2*x^5-(2/25)鈭玪nxdx^5,浠ヤ笅绗簩娆′娇鐢ㄥ垎閮ㄧН鍒嗘硶...
绛旓細鈭(1/x^3)dx=鈭玿^(-3)dx=[1/(-2)]x^(-2)+c=-1/(2x^2)+c銆俢涓哄父鏁般
绛旓細涓嶅畾绉鍒嗚В绛旀楠 鈭 arctan鈭x dx =x.arctan鈭歺 - (1/2)鈭 鈭歺/(1+x) dx =x.arctan鈭歺 - ( 鈭歺 - arctan鈭歺 ) + C =2x.arctan鈭歺 - 鈭歺 + C --- let u=鈭歺 2udu = dx 鈭 鈭歺/(1+x) dx =鈭 [u/(1+u^2) ] (2udu) =2鈭 u^2/(1...
绛旓細鍥犱负x^2姣斺垰x楂橀樁锛岃屼笖鈭歺涓哄崟涓鍙橀噺锛屼緷渚1锛氱殑鏂规硶鍗冲彲姹傚緱琚Н鍑芥暟鐨勭Н鍒 渚3锛氣埆锛坸-2锛塣2/(x^3)dx 瀵逛緥3鐩存帴鍒嗘媶灏卞彲浠ヤ簡涓嶅畾绉鍒嗙殑姹傝В鏂规硶 浜屻 鍏充簬骞傚嚱鏁颁笌骞傚嚱鏁颁笌甯告暟鍜岀殑姣斿肩殑绉垎闂鏂规硶 鏂规硶锛氬垎瀛愬彉閲忔瘮鍒嗘瘝鍙橀噺楂橀樁锛屽垎瀛愪负骞傚嚱鏁帮紙鍗筹細x^a锛夛紝鍒嗘瘝鐨勫舰寮忥細x^b+...
绛旓細= 1/2sinx/cos²x锛1/2ln(secx+tgx)+C 娉細瑙ｅ喅杩欎簺闂锛屾垜浠繍鐢ㄥ埌涓涓叕寮忥紝鍗筹細鈭1/cos^nx路dx=1/(n-1)sinx/cos^(n-1)x+(n-2)/(n-1)鈭1/cos^(n-2)x路dx 杩欎釜鍏紡鐨勮瘉鏄庡彲浠ヨ繍鐢ㄥ垎閮ㄧН鍒嗘硶缁撳悎鍥炴函姹傜Н鍒嗘硶鏉ヨ瘉鏄庛傝瘉鏄庡氨鐣ュ幓鍚с傝繕鏈夛紝妤间笂鐨勫洖绛旂畻浠涔堝憖锛岃帿鍚...
绛旓細浠=x^(1/3)鍒 x=u^3锛宒x=3u^2du 浜庢槸鈭玡^[x^(1/3)]dx=3鈭玼^2*e^udu=3鈭玼^2de^u =3u^2*e^u-6鈭玼e^udu=3u^2*e^u-6鈭玼de^u =3u^2*e^u-6ue^u+6鈭玡^udu=3(u^2-2u+2)e^u+C =3[x^(2/3)-2x^(1/3)+2]e^[x^(1/3)]+C 璁綠(x)鏄痜(x)鐨勫彟涓...
绛旓細1銆傗埆x^3(lnx)^2dx杩欐槸涓涓眰骞傚嚱鏁皒^3涓庡鏁板嚱鏁(lnx)^2鐨勪箻绉鐨勪笉瀹氱Н鍒,蹇呴』鍏堝皢骞傚嚱鏁皒^3鍑戝井鍒,鍗冲皢x^3绉诲埌寰垎鍙穌鍚庨潰,鍗硏^3dx=d[(1/4)x^4],杩欓噷鍘熷紡=鈭(lnx)^2d[(1/4)x^4],鎺ョ潃鐢ㄥ叕寮忊埆udv=uv-鈭玽d u 浜庢槸锛屽師寮=(1/4)x^4(lnx)^2-鈭(1/4)x^4d[lnx)^2...
绛旓細杩囩▼濡備笅锛氬畾绉垎鏄竴涓暟锛岃涓嶅畾绉鍒嗘槸涓涓〃杈惧紡锛屽畠浠粎浠呮槸鏁板涓婃湁涓涓绠楀叧绯汇備竴涓嚱鏁帮紝鍙互瀛樺湪涓嶅畾绉垎锛岃屼笉瀛樺湪瀹氱Н鍒嗭紝涔熷彲浠ュ瓨鍦ㄥ畾绉垎锛岃屾病鏈変笉瀹氱Н鍒嗐
绛旓細姹備竴涓涓嶅畾绉鍒X涔樻牴鍙蜂笅(1-x骞虫柟)(1+x骞虫柟) 鈭玿[(1-x^2)(1+x^2)]^(1/2)dx =(1/2)鈭玔1-(x^2)^2]^(1/2)d(x^2) =(1/2)鈭(1-t^2)^(1/2)dt t=x^2 璁総=sinu 0鈮鈮i/2 鈭村師寮=(1/2)鈭玞osu*cosudu =(1/4)鈭(cos2u+1)du =sin2u/8+u...
