微积分求解:∫sin^3 (x) cos^2 (x) dx 如题.

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微积分求解:∫sin^3 (x) cos^2 (x) dx 如题.
微积分求解:∫sin^3 (x) cos^2 (x) dx
如题.

微积分求解:∫sin^3 (x) cos^2 (x) dx 如题.
∫sin^3 (x) cos^2 (x) dx
=∫sin^2 (x) cos^2 (x)sin(x)dx
=-∫sin^2 (x) cos^2 (x)dcos(x)
=∫[cos^2 (x)-1]cos^2 (x)dcos(x)
设cos(x)=u
上式=∫(u^2-1)u^2du
=∫(u^4-u^2)du
=(u^5)/5-(u^3)/3+C
=cos^5(x)/5-cos^3(x)/3+C