∫1/(4x^2+4x+10)dx
=∫1/(4x^2 + 4x + 1 + 9)dx
=∫1/[(2x+1)^2 + 3^2]dx
=1/2∫1/[(2x+1)^2 + 3^2]d(2x+1)
=1/6arctan(2x+1)/3 + C