一道不定积分的题∫x*( sin(x/2) )^2 dx
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一道不定积分的题
∫x*( sin(x/2) )^2 dx
∫x*( sin(x/2) )^2 dx
![一道不定积分的题∫x*( sin(x/2) )^2 dx](/uploads/image/z/4225846-22-6.jpg?t=%E4%B8%80%E9%81%93%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%E7%9A%84%E9%A2%98%E2%88%ABx%2A%28+sin%28x%2F2%29+%29%5E2+dx)
原式=∫x(1-cosx)/2 dx
=∫x/2 dx-1/2*∫xcosxdx
=x²-1/2(xcosx-∫cosxdx)
=x²-(1/2)xcosx+(1/2)sinx+C
=∫x/2 dx-1/2*∫xcosxdx
=x²-1/2(xcosx-∫cosxdx)
=x²-(1/2)xcosx+(1/2)sinx+C