设函数f(x)有一个原函数为xe∧-x∧2,则∫f(cos(3x)sin(3x)dx=( )?

2024-12-20 17:03:11
推荐回答(1个)
回答1:

∫f[cos(3x)]sin(3x)dx = -(1/3)∫f[cos(3x)]dcos3x, (u = cos3x)
= -(1/3)∫f(u)du = -(1/3)ue^(-u^2) + C
= -(1/3) cos3x e^[-(cos3x)^2] + C