∫x/(x^2+3x+3)dx

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∫x/(x^2+3x+3)dx∫x/(x^2+3x+3)dx∫x/(x^2+3x+3)dx∫x/(x^2+3x+3)dx=∫(x+3/2-3/2)/(x^2+3x+3)dx=∫(x+3/2)/(x^2

∫x/(x^2+3x+3)dx
∫x/(x^2+3x+3)dx

∫x/(x^2+3x+3)dx
∫x/(x^2+3x+3)dx
=∫(x+3/2-3/2)/(x^2+3x+3)dx
=∫(x+3/2)/(x^2+3x+3)dx-3/2∫dx/(x^2+3x+3)
=1/2∫d(x^2+3x+3)/(x^2+3x+3)-3/2∫dx/(x+3/2)^2+(√3/2)^2
=ln(x^2+3x+3)/2-√3arctan(√3x/2)+C