# Calculating Triple Integrals – Bounded by surfaces – Exercise 4573

Exercise

Calculate the integral

$$\int\int\int_T \frac{1}{{(1+x+y+z)}^3} dxdydz$$

Where T is bounded by the surfaces

$$x=0,y=0,z=0,x+y+z=1$$

$$\int\int\int_T \frac{1}{{(1+x+y+z)}^3} dxdydz=\frac{1}{2}\ln 2-\frac{5}{16}$$