Let I = ∫x dxx + 4=∫x + 4 - 4x + 4 dx=∫x+4x + 4 dx - 4 ∫dxx + 4=∫x + 4 dx - 4∫x+4-1/2 dx=23x+43/2 - 8 x + 4 + C

∫x/√x+4dx

Let I = \int \frac{x d x}{\sqrt{x + 4}} = \int \frac{x + 4 - 4}{\sqrt{x + 4}} d x = \int \frac{x + 4}{\sqrt{x + 4}} d x - 4 \int \frac{d x}{\sqrt{x + 4}} = \int \sqrt{x + 4} d x - 4 \int {(x + 4)}^{- 1 / 2} d x = \frac{2}{3} {(x + 4)}^{3 / 2} - 8 \sqrt{x + 4} + C