Integrate 5cos(3x - 1) with respect to x

Firstly, we may simplify the expression by factoring out any constants. In this case 5 can be factored out. 

5 ∫ cos(3x-1) dx 

For the integrand cos(3x -1), we can use a simple u-substitution. Where u = 3x -1 and du = 3dx. 

Our integral is then simplified to 5 ∫ cos(u) du/3

The integral of cos(u) is equal to sin(u)

And therefore the solution becomes: (5/3)*sin(u) + constant

Subsituting for u: (5/3)*sin(3x-1) + constant