Help with homework. Integrate: (x^-2 + cos(5x))dx

I am stuck on this problem and would like a step by step explanation of how to get the answer please. Thank you.

∫ x⁻² + cos(5x) dx=
=∫ 1/x² dx+ ∫ cos(5x) dx=
=-1/x + ⅕∫ cos(5x) d(5x)=
=-1/x + ⅕sin(5x) +C

I think
∫ (x^(-2) + cos 5x) dx
∫ x⁻² + cos(5x) dx
=∫ 1/x² dx+ ∫ cos(5x) dx=
=-1/x + ⅕∫ cos(5x) d(5x)=
=-1/x + ⅕sin(5x) +C

x^(-2+1)/(-2+1) + (1/5)sin(5x)

i left the first bit unsimplified so you could visualize it better.

∫ (x^(-2) + cos 5x) dx = -1/x + 1/5 sin 5x + C

why do i keep drooling milk?