∫sin³xdx等于多少

∫sin³xdx等于多少
∫sin³xdx等于多少

∫sin³xdx等于多少
原式=∫sinsin²xdx
=-∫(1-cos²x)dcosx
=cos³x/3-cosx+C

∫(sinx)^3dx
=∫(sinx)^2*sinxdx
= -∫sin^2xd(cosx)
= -∫(1-cos^2x)d(cosx)
= -cosx+1/3*(cosx)^3+C

In[1]:= \[Integral]{{Sin[x]}^3} \[DifferentialD]x
Out[1]= {{-((3 Cos[x])/4) + 1/12 Cos[3 x]}}