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1/(Cos^4xsinx)Dx議音協持蛍

-ln(cos(x/2))+ln(sin(x/2))+sec(x)+(sec(x))^3 /3 +C

辛參泌夕幟化介醴抓嬶蛍柴麻.将蔀方僥妖錦逸低盾基,萩式扮寡追.仍仍!

音協持蛍sin^4xcos^4xdx=1/16*s(sin2x)^4 dx=1/64*s(1-cos4x)^2 dx=1/64*s(1-2cos4x+(cos4x)^2)dx=1/64*(sdx-s2cos4xdx+1/2*s(1+cos8x)dx)=1/64*x-1/128*sin4x+1/128*sdx+1/128*scos8xdx=x/64-1/128*sin4x+x/128+1/1024*sin8x+c=3x/128-1/128*sin4x+1/1024*sin8x+c

〈1/cos^4xdx=tanx+1/3tan^3x+C.C葎械方.盾基狛殻泌和:〈1/cos^4xdx=〈sec^4xdx=〈sec^2xd(tanx)=〈(1+tan^2x)d(tanx)=tanx+1/3tan^3x+C 制婢彿創:揖叔眉叔痕方議児云購狼塀 宜方購狼:tanα cotα=1、sinα cscα=1、cosα secα=1;斌

盾:cos^2x=(1+cos2x)/2,侭參〈cos^2x dx =〈(1+cos2x)/2dx=x/2+sin2x/4+c,c葎持蛍械方.

〈(cosx)^4 dx=〈(1-sinx^2)cosx^2dx=〈cosx^2dx-〈sinx^2cosx^2dx=〈(1/2)(1+cos2x)dx-〈(1/4)[(1-cos4x)/2]dx=(x/2)+(1/4)sin2x-(x/8)+(1/32)sin4x+C =3x/8+(1/4)sin2x+(1/32)sin4x+C

〈1/(sin^4xcos^4x)dx=〈16/sin^4(2x)dx=〈16csc^4(2x)dx=〈16[cot^(2x)+1]csc^2(2x)dx=-〈8[cot^2(2x)+1]dcot(2x)=-8/3cot^3(2x)-8cot(2x)+C

盾: 〈[sinxcosx/(sinx+cosx)]dx =〈[sinxcosx/(1-2sinxcosx)]dx =1/2〈[1/(〔2sinxcosx-1)-1/(〔2sinxcosx+1)]dsinxcosx =1/2〈[1/(〔2sinxcosx-1)]d(sinxcosx)-1/2〈[1/(〔2sinxcosx+1)]d(sinxcosx) =(〔2/4)ln(〔2sinxcosx-1)-(〔2/4)ln(〔2sinxcosx+1) =(〔2/4)ln[(〔2sinxcosx-1)/(〔2sinxcosx+1)]+C 參貧! 錬李斤低嗤侭逸廁!

〈 1/[(sinx)^4(cosx)^4] dx=16〈 1/(2sinxcosx)^4 dx=16〈 1/(sin2x)^4 dx=16〈 (csc2x)^4 dx=-8〈 csc2x d(cot2x)=-8〈 (cot2x+1) d(cot2x)=-(8/3)cost2x - 8cot2x + C ‐方僥岻胆/妖錦葎艇盾基,飛嗤音峡萩弖諒,泌惚盾畳諒籾萩泣和中議^僉葎諾吭基宛 ̄.

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