高数计算不定积分,第10题我不会,用什么方法解最好?请高手详解一下解题过程。 大一高数不定积分这块题怎么算啊,都不会,用什么方法
\u9ad8\u6570\u8ba1\u7b97\u4e0d\u5b9a\u79ef\u5206\uff0c\u7b2c11\u9898\u6211\u4e0d\u4f1a\uff0c\u7528\u4ec0\u4e48\u65b9\u222b(x^2-x)lnxdx
=\u222bx^2lnxdx-\u222bxlnxdx
=\u222b lnx d(x³/3)-\u222b lnx d(x²/2)
= x³/3 lnx - \u222bx³/3dlnx - (1/2)x²lnx + (1/2)\u222b x² d(lnx)
=1/3x³lnx-\u222b1/3x²dx - (1/2)x²lnx + (1/2)\u222b x dx
=1/3x³lnx-1/3\u00d71/3x³ - (1/2)x²lnx + (1/2)(x²/2)+C
=1/3x³lnx-1/9x³-(1/2)x²lnx + (1/4)x²+C
\u79ef\u5206\u6cd5\u5219\uff0c\u79ef\u5206\u65b9\u6cd5\uff0c\u7c7b\u578b\u9898
=1-sin^2(0.5x)
=(cos(2(0.5x))+1)/2
=(cosx+1)/2
则:原式=0.5*∫(cosx+1)dx=0.5*∫cosxdx+0.5x=0.5sinx+0.5x+C
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