求不定积分,详细过程
方法如下,请作参考:
若有帮助,
请采纳。
(2)
f(x) =x^2.(sinx)^5
f(-x) =-f(x)
f(x) 是奇函数
∫(-a->a) f(x) dx =0
=>
∫(-1->1) x^2.(sinx)^5 dx =0
(3)
f(x) = x^4.sinx
f(-x) =-f(x)
f(x) 是奇函数
∫(-a->a) f(x) dx =0
=>∫(-1->1) x^4.sinx dx =0
(1)原式=∫x^(-1/2)dx
=2*x^(1/2)+C,其中C是任意常数
(2)原式=2*∫tan(√x+1)d(√x+1)
=2*ln|sec(√x+1)|+C,其中C是任意常数
(3)原式=∫(sec^2x-1)dx
=tanx-x+C,其中C是任意常数
(4)原式=(1/2)*∫2sin(x/2)cos(x/2)dx
=(1/2)*∫sinxdx
=(-1/2)*cosx+C,其中C是任意常数
(5)原式=∫(1-2lnx)d(lnx)
=lnx-(lnx)^2+C,其中C是任意常数
绛旓細01.** 涓嶅畾绉垎瀹為檯涓婃槸鍘熷嚱鏁鐨姒傚康寤朵几銆傚鏋滃嚱鏁癨( F(x) \)鏄嚱鏁癨( f(x) \)鐨勪竴涓鍘熷嚱鏁帮紝閭d箞\( F'(x) = f(x) \)銆傚師鍑芥暟鍖呭惈浜嗙Н鍒嗙鍙枫佽绉嚱鏁颁互鍙婅绉〃杈惧紡銆02.** 涓嶅畾绉垎鎸囩殑鏄嚱鏁癨( f(x) \)鍦ㄦ煇涓尯闂村唴鐨勬墍鏈夊師鍑芥暟鐨勬荤О锛岄氬父琛ㄧず涓篭( \int f(x) \,...
绛旓細鎶婂嚱鏁癴锛坸锛夌殑鎵鏈夊師鍑芥暟F锛坸锛+C锛圕涓轰换鎰忓父鏁帮級鍙仛鍑芥暟f锛坸锛夌殑涓嶅畾绉垎锛璁颁綔锛屽嵆鈭玣锛坸锛塪x=F锛坸锛+C.鍏朵腑鈭彨鍋氱Н鍒嗗彿锛宖锛坸锛夊彨鍋氳绉嚱鏁帮紝x鍙仛绉垎鍙橀噺锛宖锛坸锛塪x鍙仛琚Н寮忥紝C鍙仛绉垎甯告暟锛屾眰宸茬煡鍑芥暟涓嶅畾绉垎鐨勮繃绋鍙仛瀵硅繖涓嚱鏁拌繘琛岀Н鍒嗐傛敞锛氣埆f锛坸锛塪x+c1=鈭玣锛坸锛...
绛旓細鏂规硶濡備笅锛岃浣滃弬鑰冿細鑻ユ湁甯姪锛岃閲囩撼銆
绛旓細=鈭1/sinxdx =鈭1/[2sin(x/2)cos(x/2)]dx锛屼袱鍊嶈鍏紡 =鈭1/[sin(x/2)cos(x/2)]d(x/2)=鈭1/tan(x/2)*sec²(x/2)d(x/2)=鈭1/tan(x/2)d[tan(x/2)]锛屾敞鈭玸ec²(x/2)d(x/2)=tan(x/2)+C =ln|tan(x/2)|+C銆傝鐐瑰嚮杈撳叆鍥剧墖鎻忚堪 渚嬪涓嶅畾绉垎...
绛旓細鏂规硶濡備笅锛岃浣滃弬鑰冿細
绛旓細锛1锛夊師寮=鈭玔x^(3/2)+1-x-x^(-1/2)]dx =(2/5)*x^(5/2)+x-(1/2)*x^2-2x^(1/2)+C 锛2锛夊師寮=(1/ln10)*10^x+3sinx+2x^(1/2)+C 锛3锛夊師寮=鈭玔2/鈭(1-x^2)-1]dx =2arcsinx-x+C 锛4锛夊師寮=鈭玠x/2cos^2x =(1/2)*鈭玸ec^2xdx =(1/2)*tanx+C...
绛旓細濂囧嚱鏁绉垎=0 鏂规硶濡備笅锛岃浣滃弬鑰冿細
绛旓細瑙:杩欎釜寰楀叿浣撴儏鍐靛叿浣撳垎鏋愶紝璇锋妸鍏蜂綋鐨勪笉瀹氱Н鍒鍏紡棰樼洰鍙戣繃鏉ワ紝鎴戠湅鐪嬨傛渶濂芥槸鍥剧墖锛岃繖鏍锋瘮杈冪洿瑙傛柟渚胯绠椼備緥濡:涓嬪浘 瑙e父寰垎鏂圭▼ 瑙e父寰垎鏂圭▼ 璇峰弬鑰冿紝甯屾湜瀵逛綘鏈夊府鍔╋紒
绛旓細1銆佺绫绘崲鍏冩硶 鈭1/(1+e^x)dx锛濃埆e^(-x)/(1+e^(-x))dx锛-鈭1/(1+e^(-x))d(1+e^(-x))锛-ln(1+e^(-x))锛婥锛-ln((1+e^x)/e^x)锛婥锛漻-ln(1+e^x)锛婥 鎴 鈭1/(1+e^x)dx锛濃埆 [1 - e^x/(1+e^x))dx锛漻-鈭1/(1+e^x)d(1+e^x)锛漻-ln(1+...
绛旓細01 鎯宠姹備笉瀹氱Н鍒棣栧厛瑕佷簡瑙d粈涔堟槸鍘熷嚱鏁帮紝鍗冲湪瀹氫箟鍩烮涓彲瀵煎嚱鏁癋鐨勫鍑芥暟涓篺,鍒欑ОF涓篺鐨勫師鍑芥暟锛屽師鍑芥暟鐨勫熀鏈蹇靛涓嬶細02 涓嶅畾绉垎鏄寚瀹氫箟鍩熷唴锛屽嚱鏁癴鐨勬墍鏈夊師鍑芥暟锛屼竴鑸敱绉垎绗︺佽绉垎鍑芥暟銆佽绉垎琛ㄨ揪寮忕瓑缁勬垚锛屽熀鏈蹇靛涓嬶細浜屻佸熀鏈Н鍒嗚〃 01 涓轰簡鑳藉鍦ㄨВ棰樻椂蹇熺殑姹傚嚭绉垎闂锛屾垜浠...