求不定积分 1.∫(x√X+1/X²)dx 2.∫xe^xdx 3.∫x²1nxdx 4.∫xcos x/2dx

求不定积分 1.∫(x√X+1/X²)dx 2.∫xe^xdx 3.∫x²1nxdx 4.∫xcos x/2dx
求不定积分 1.∫(x√X+1/X²)dx 2.∫xe^xdx 3.∫x²1nxdx 4.∫xcos x/2dx

求不定积分 1.∫(x√X+1/X²)dx 2.∫xe^xdx 3.∫x²1nxdx 4.∫xcos x/2dx
1.∫(x√x+1/x^2) dx
=∫ x^(3/2) dx+∫x^(-2) dx
=(2/5)x^(5/2)+(-1)x^(-1)+C
=(2/5)x^(5/2)-x^(-1)+C
2.∫ xe^x dx
=∫ x d(e^x)
=xe^x-∫ e^x dx
=xe^x-e^x+C
=(x-1)e^x+C
3.∫ x^2lnx dx
=(1/3)*∫ lnx d(x^3)
=(1/3)*lnx*(x^3)-(1/3)∫ x^3 d(lnx)
=(1/3)x^3*lnx-(1/3)∫ x^2 dx
=(1/3)x^3*lnx-(1/9)x^3+C
4.∫ xcos(x/2) dx
=2*∫ xcos(x/2) d(x/2)
=2*∫ x d(sin(x/2))
=2xsin(x/2)-2*∫ sin(x/2) dx
=2xsin(x/2)-4*∫ sin(x/2) d(x/2)
=2xsin(x/2)+4cos(x/2)+C
有不懂欢迎追问