Integral of (sinx+5)dx dx

1. Integrate term-by-term:

   1. The integral of sine is negative cosine:

      $$\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$$

   1. The integral of a constant is the constant times the variable of integration:

      $$\int 5\, dx = 5 x$$

   The result is: $5 x - \cos{\left(x \right)}$

2. Add the constant of integration:

   $$5 x - \cos{\left(x \right)}+ \mathrm{constant}$$

The answer is:

$$5 x - \cos{\left(x \right)}+ \mathrm{constant}$$