Integral of cos0,5x dx

1. Let $u = 0.5 x$.

   Then let $du = 0.5 dx$ and substitute $2.0 du$:

   $$\int 2.0 \cos{\left(u \right)}\, du$$

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

      $$\int \cos{\left(u \right)}\, du = 2.0 \int \cos{\left(u \right)}\, du$$

      1. The integral of cosine is sine:

         $$\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$$

      So, the result is: $2.0 \sin{\left(u \right)}$

   Now substitute $u$ back in:

   $$2.0 \sin{\left(0.5 x \right)}$$

2. Add the constant of integration:

   $$2.0 \sin{\left(0.5 x \right)}+ \mathrm{constant}$$

The answer is:

$$2.0 \sin{\left(0.5 x \right)}+ \mathrm{constant}$$