正弦函数三次方的原函数是多少?

2024-12-04 20:13:31
推荐回答(2个)
回答(1):

∫(sinx)^3dx
=∫(sinx)^2sinxdx
=-∫[1-(cosx)^2dcosx
=-∫1dcosx+∫(cosx)^2dcosx
=-cosx+(cosx)^3/3+C

回答(2):

∫sin³xdx
=∫sin²x*sinxdx
=-∫(1-cos²x)dcosx
=-cosx+cos³x/3+C