请问这个不定积分怎么求？谢谢！ 请问这个不定积分后边怎么求？谢谢
\u8bf7\u95ee\u8fd9\u4e2a\u4e0d\u5b9a\u79ef\u5206\u600e\u4e48\u6c42\uff1f\u8c22\u8c22\u5927\u4f6c\uff01\u6362\u5143\u79ef\u5206\u6cd5
=sqrt(x^2-1)d(x^2)/2
=sqrt(t-1)dt/2
=(t-1)^1.5/3+C
\u7b2c\u4e00\u4e2a\u90e8\u5206\u6709\u516c\u5f0f\u7684.
解答过程如下
绛旓細鈭玸inxdx/x =-鈭玠cosx/x=-cosx/x+鈭玞osxd(1/x)=-cosx/x+鈭玠sinx/x^2 =-cosx/x+sinx/x^2+2鈭玸inxdx/x^3 =-cosx/x+sinx/x^2-2cosx/x^3+2鈭玞osxd(1/x^3)=-cosx/x+sinx/x^2-2cosx/x^3+6sinx/x^4+24鈭玸inxdx/x^5 =-cosx/x+sinx/x^2-2cosx/x^3+6sinx/x^4...
绛旓細鎹㈠厓t=2x+1 =鈭(2x-4)/(4x²+4x+2)²d(2x+1)=鈭(t-5)/(t²+1)²dt =1/2鈭1/(t²+1)²d(t²+1)-5鈭1/(tan²u+1)²dtanu =-1/2(t²+1)-5鈭玞os²udu =-1/4(2x²+2x+1)-5/2鈭(cos2u+1)du...
绛旓細涓嶅畾绉垎鏄眰涓涓嚱鏁扮殑鍘熷嚱鏁鎴栧弽瀵兼暟鐨勮繃绋嬨傜粰瀹氬嚱鏁癴锛坸锛=xsinx锛屾垜浠渶瑕佹壘鍒杩欎釜鍑芥暟鐨勫師鍑芥暟銆傛牴鎹笉瀹氱Н鍒嗙殑璁＄畻娉曞垯锛屾垜浠彲浠ュ皢f锛坸锛=xsinx鍒嗚В涓轰袱閮ㄥ垎锛氱涓閮ㄥ垎鏄痵inx锛岃繖鏄竴涓凡鐭ュ嚱鏁帮紝鍏朵笉瀹氱Н鍒嗗凡缁忕煡閬擄紝鍗硈inx+C1銆傜浜岄儴鍒嗘槸x锛岃繖鏄竴涓竴娆″嚱鏁帮紝鍏朵笉瀹氱Н鍒嗘槸1/2*x^2...
绛旓細浠=sint==>dx=costdt锛宻qrt(1-x^2)=cost==> 鍘熷紡=inf(dt/sint),杩鏄竴涓熀鏈殑绉垎=ln(csct-cott)csct=1/sint=1/x锛宑ott=sqrt(1-x^2)/x ==>鍘熷紡绉垎=ln[1-sqrt(1-x^2)]-ln|x|+C
绛旓細鏈绠鍗曠殑鏂规硶灏辨槸鎹㈠厓锛屾垨鑰呯洿鎺ユ煡绉垎琛ㄣ
绛旓細I = 鈭玿|cosxsinx|dx = (1/2)鈭玿|sin2x|dx 褰 2k蟺 鈮 2x 鈮 2k蟺+蟺锛 鍗 k蟺 鈮 x 鈮 k蟺+蟺/2 鏃 I = (1/2)鈭玿sin2xdx = - (1/4)鈭玿dcos2x = - (1/4)xcos2x + (1/4)鈭玞os2xdx = - (1/4)xcos2x + (1/8)sin2x + C 褰 2k蟺-蟺 鈮 2x 鈮 2k...
绛旓細閫夐」A姝ｇ‘锛岃繃绋嬩笌缁撴灉濡傚浘鎵绀虹殑锛
绛旓細鍒嗕袱姝ュ嵆鍙畻鍑锛侊紒锛
绛旓細鈭玔(3x⁴-3x²+5x²)/(1+x)]dx =鈭玔(3x⁴-3x²+5x²)/(1+x)]dx =鈭玔3x²(x-1)+(5x²-5+5)/(1+x)]dx =鈭玔3x³-3x²+5x-5+5/(1+x)]dx =¾x⁴-x³+2.5x²-5x+5ln|x+1|+C ...
绛旓細鍥炵瓟锛氬垎瀛愬垎姣嶅悓闄や互cos²x,寰 鍘熷紡=鈭玸ec²x/(sec²x+tan²x)dx =鈭1/(2tan²x+1)dtanx =1/鈭2 鈭1/[(鈭2tanx)²+1] d(鈭2tanx) =鈭2/2 arctan(鈭2tanx)+c
