Integral of sqrt(5-x) dx

1. Let $u = 5 - x$.

   Then let $du = - dx$ and substitute $- du$:

   $$\int \left(- \sqrt{u}\right)\, du$$

   1. The integral of a constant times a function is the constant times the integral of the function:

      $$\int \sqrt{u}\, du = - \int \sqrt{u}\, du$$

      1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$:

         $$\int \sqrt{u}\, du = \frac{2 u^{\frac{3}{2}}}{3}$$

      So, the result is: $- \frac{2 u^{\frac{3}{2}}}{3}$

   Now substitute $u$ back in:

   $$- \frac{2 \left(5 - x\right)^{\frac{3}{2}}}{3}$$

2. Add the constant of integration:

   $$- \frac{2 \left(5 - x\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}$$

The answer is:

$$- \frac{2 \left(5 - x\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}$$