This integral is solved by using the power rule. Move the the constant –4 to the outstide of the integral, then convert the radical √x to a fractional exponent and convert the fraction 1/x to a negative exponent x–1. Combine the two exponents x1/2·x–1 = x–1/2 and solve –4 ∫ x–1/2dx using the power rule with n = –1/2. Since n + 1 = 1/2, we get

∫ –4   x
x
  dx
=  –4 ∫ x1/2 x–1 dx
=  –4 ∫ x–1/2 dx
=  –4   1
1/2
  x1/2  + C
=  –8√x  + C