求不定积分,∫xsin²xdx.
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![求不定积分,∫xsin²xdx.](/uploads/image/z/10265486-14-6.jpg?t=%E6%B1%82%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%2C%E2%88%ABxsin%26%23178%3Bxdx.)
求不定积分,∫xsin²xdx.
求不定积分,∫xsin²xdx.
求不定积分,∫xsin²xdx.
[x²/2-xsin(2x)/2-cos(2x)/4]'
=x-sin(2x)/2-xcos(2x)+sin(2x)/2
=x-xcos(2x)
∫xsin²xdx=∫x[1-cos(2x)]/2 dx
=(1/2)∫[x-xcos(2x)]dx
=(1/2)[x²/2-xsin(2x)/2-cos(2x)/4]+C
=x²/4- xsin(2x)/4- cos(2x)/8 +C