求不定积分,xsin^2x

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求不定积分,xsin^2x
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求不定积分,xsin^2x
求不定积分,xsin^2x

求不定积分,xsin^2x
∫x(sinx)^2dx
=(1/2)∫x(1-cos2x)dx
=(1/4)x^2-(1/4)∫xdsin2x
=(1/4)x^2-(1/4)(xsin2x)+(1/4)∫sin2xdx
=(1/4)x^2-(1/4)(xsin2x)+(-1/8)cos2x+C

对不定积分做两次分部积分(内容长,略),最后得: I=(-8/17)*sin(x/2)*e^(-2x)-(2/17)*cos(x/2)*e^(-2x) I=∫e^(-2x)sin(x