求不定积分 ∫(sin^5x sin^2x)dx

原式=∫((sinx)^5+(sinx)^2)dx
=-∫(1-(cosx)^2)^2d(cosx)+(1/2)∫(1-cos2x))dx
=-∫(1-2(cosx)^2+(cosx)^4)d(cosx)+(1/2)∫(1-cos2x))dx
=-(cosx-(2/3)(cosx)^3+(1/5)(cosx)^5)+(1/2)(x-(1/2)sin2x)+C
=(-1/5)(cosx)^5+(2/3)(cosx)^3-cosx+x/2-(1/4)sin2x+C
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