求sinx^2cosx^3的不定积分

(sinx)^2(cosx)^3
2024-11-03 01:34:30
推荐回答(2个)
回答1:

(cosx)^2(sinx)^3 的不定积分
∫(cosx)^2(sinx)^3 dx
=-∫(cosx)^2(sinx)^2 dcosx
=-∫(cosx)^2(1-(cosx)^2) dcosx
= -[ (cosx)^3/3- (cosx)^5/5] + C

回答2:

∫sin²xcos³xdx
=∫sin²xcos²xd(sinx)
=∫sin²x(1-sin²x)d(sinx)
=∫(sin²x-sin⁴x)d(sinx)
=(1/3)sin³x -(1/5)(sinx)^5 +C