请问这几道不定积分题怎么做 请问这道不定积分题怎么做
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1\u3001=(1-cosx)/2dx\uff0c\u79ef\u5206
2\u3001=(x+4)/(x^2+4x+3)-2/(x^2+4x+3)\uff0c\u5bf92/(x^2+4x+3)\u8fdb\u884c\u591a\u9879\u5f0f\u5206\u89e3
3\u3001=(2-x^2)^100d(x^2)/2\uff0c\u79ef\u5206\u5c31\u51fa\u6765\u4e86
4\u3001=d(e^x)/sqrt(e^x+1)\uff0c\u79ef\u5206\u5c31\u51fa\u6765\u4e86
5\u3001=d(lnx)/lnx=ln(lnx)+C
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∫sinx^8dx=x*sinx^8-∫xd(sinx^8)=x*sinx^8-8∫x^8*cosx^8dx=x*sinx^8-8∫x^8*(1-sinx^8)dx=x*sinx^8-8∫x^8dx+8∫x^8*sinx^8dx=x*sinx^8-8/9*x^9+8∫x^8*sinx^8dx，
8∫x^8*sinx^8dx=∫x*sinx^8d(x^8)=∫x*d(cosx^8)=-x*cosx^8+∫cosx^8dx=-x*cosx^8+∫(1-sinx^8)dx=-x*cosx^8+∫dx-∫sinx^8dx=-x*cosx^8+x-∫sinx^8dx，
∫sinx^8dx=x*sinx^8-8/9*x^9-x*cosx^8+x-∫sinx^8dx，2∫sinx^8dx=x*sinx^8-8/9*x^9-x*cosx^8+x，∫sinx^8dx=1/2*x*sinx^8-4/9*x^9-1/2*x*cosx^8+1/2*x+C。
∫x^2*cos^2xdx=1/2*∫x^2(cos2x+1)dx=1/2*∫x^2*cos2xdx+1/2*∫x^2dx=1/4*∫x^2*cos2xd(2x)+1/6*x^3=1/4*∫x^2d(sin2x)+1/6*x^3=1/4*x^2*sin2x-1/4*∫2x*sin2xdx+1/6*x^3=1/4*x^2*sin2x-1/4*∫x*sin2xd(2x)+1/6*x^3=1/4*x^2*sin2x+1/4*∫xd(cos2x)+1/6*x^3=1/4*x^2*sin2x+1/4*x*cos2x-1/4*∫cos2xdx+1/6*x^3=1/4*x^2*sin2x+1/4*x*cos2x-1/8*∫cos2xd(2x)+1/6*x^3=1/4*x^2*sin2x+1/4*x*cos2x-1/8*sin2x+1/6*x^3+C。
∫(1+x)^2/(1+x^2)*dx=∫(1+x^2+2x)/(1+x^2)*dx=∫(1+x^2)/(1+x^2)*dx+∫2x/(1+x^2)*dx=∫dx+∫d(1+x^2)/(1+x^2)=x+ln|1+x^2|+C。
都不难哈
慢慢 练 练多了就会了
见图片
∫dx/x(1-x) =∫dx/x-∫d（1-x）/（1-x）=ln|x|-ln|1-x|+C
∫sinx^8 dx（是sinx的8次方还是sin（x的8次方）????）
∫x^2 * cos^2x dx =0.5∫x²（1+cos2x）dx=x³/6+0.5∫x²cos2xdx=x³/6+0.25x²sin2x-0.5∫xsin2xdx=x³/6+0.25x²sin2x-0.25xcos2x+0.5∫cos2xdx=x³/6+0.25x²sin2x-0.25xcos2x+0.25sin2x+C
∫(1+x)^2 / (1+x^2) =∫(1+2x/(1+x²)）dx=x+ln|1+x²| +C
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