Solved integral of the form ∫(αx+β)cosγxdx

Solving an indefinite integral of the form ∫(αx+β)cosγxdx by the method of integration by parts, where α takes the values ±1,±2,±3,±4,±5,…m; β takes the values ±1,±2,±3,±4,±5,…n; γ takes the values 1,2,3,4,5,…p.
An example of solving integrals for α=3, β=−2, γ=4 is considered; α=1, β=−5, γ=2; α=4, β=2, γ=1; α=2, β=3, γ=3;

∫(αx+β)cosγxdx, ∫(3x−2)cos4xdx, ∫(x−5)cos2xdx, ∫(4x+2)cosxdx, ∫(2x+3)cos3xdx

The solution is in PDF format