微积分公式大全97241

微积分公式Dx sin x=cos x cos x = -sin x tan x = sec2 x cot x = -csc2 x sec x = sec x tan x csc

微积分公式 -1-1 sinxdx=-cosx+C Dsinx=cosx sin(-x)=-sinx x -1-1 cosxdx=sinx+C cosx=-sinx cos(-x)=-cosx 2 -1-1 tanxdx=ln|secx|+C tanx=secx tan(-x)=-tanx 2 -1-1 cotxdx=ln|sinx|+C cotx=-cscx cot(-x)=-cotx -1-1 secxdx=ln|secx+tanx|+C secx=secxtanx sec(-x)=-secx -1-1 cscxdx=ln|cscx–cotx|+C cscx=-cscxcotx csc(-x)=-cscx -1-1 sinxdx=xsinx++C -1 sinh()=ln(x+)xR -1 -1-1 Dsin()= cosxdx=xcosx-+C x -1-12 -1 tanxdx=xtanx-½ln(1+x)+C cosh()=ln(x+)x1 ≧ -1 cos()= -1-12 cotxdx=xcotx+½ln(1+x)+C -1 tanh()=ln()|x|<1 -1-1 secxdx=xsecx-ln|x+ -1 tan()= -1 |+C coth()=ln()|x|>1 -1 cot()= -1-1 cscxdx=xcscx+ln|x+ -1 |+C sech()=ln(+)0x ≦≦1 -1 sec()= -1 csc(x/a)= -1 csch()=ln(+)|x|>0 sinhxdx=coshx+C Dsinhx=coshx uvuvvu d=d+d x coshxdx=sinhx+C coshx=sinhx uvuvuvvu d==d+d 2 tanhxdx=ln|coshx|+C tanhx=sechx uvuvvu d=-d → 2 22 cothxdx=ln|sinhx|+C cothx=-cschx cosθ-sinθ=cos2θ -1-x 22 e sechxdx=-2tan()+C sechx=-sechx cosθ+sinθ=1 22 tanhx coshθ-sinhθ=1 22 cschx=-cschx coshθ+sinhθ=cosh2θ cschxdx=2ln||+C cothx 3 sin3θ=3sinθ-4sinθ -1-1 sinhxdx=xsinhx-+C 3 cos3θ=4cosθ-3cosθ -1 Dsinh()= x 3 →sinθ=¼(3sinθ-sin3θ) -1-1 coshxdx=xcoshx-+C 3 →cosθ=¼(3cosθ+cos3θ) -1-1 tanhxdx=xtanhx+½ln| -1 cosh()= 2 1-x|+C sinx=cosx= -1-1 cothxdx=xcothx-½ln| 2 -1 1-x|+C tanh()= -1-1-1 sechxdx=xsechx-sinx+C -1-1-1 -1 cschxdx=xcschx+sinhx+ coth()= C sinhx=coshx= γ a