∫x+1/(x2+3x+5)dx

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∫x+1/(x2+3x+5)dx∫x+1/(x2+3x+5)dx∫x+1/(x2+3x+5)dx∫x+1/(x2+3x+5)dx=1/2∫(2x+3)/((x+3/2)^2+11/4)dx-1/2∫1

∫x+1/(x2+3x+5)dx
∫x+1/(x2+3x+5)dx

∫x+1/(x2+3x+5)dx
∫x+1/(x2+3x+5)dx
=1/2∫(2x+3)/((x+3/2)^2+11/4)dx-1/2∫1/((x+3/2)^2+11/4)dx
=1/2∫1/((x+3/2)^2+11/4)d((x+3/2)^2)- 2/11∫1/((2√11x/11+3√11/11)^2+1)d(x+2/3)
=1/2ln(x^2+3x+5)-2/11arctan(2√11x/11+3√11/11)+C