Integral of 5cosx dx

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

   $$\int 5 \cos{\left(x \right)}\, dx = 5 \int \cos{\left(x \right)}\, dx$$

   1. The integral of cosine is sine:

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

   So, the result is: $5 \sin{\left(x \right)}$

2. Add the constant of integration:

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

The answer is:

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