Solved integral of the form ∫xsin(αx+β)dx

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

The solution is in PDF format