Solved integral of the form ∫(αx+β)sin(x/γ)dx

Solved integral of the form ∫(αx+β)sin(x/γ)dx

Solving an indefinite integral of the form ∫(αx+β)sin(x/γ)dx 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 2,3,4,5,…p.
An example of solving integrals for α=1, β=−1, γ=4 is considered; α=2, β=3, γ=3; α=3, β=−4, γ=2; α=4, β=2, γ=5;

∫(αx+β)sin(x/γ)dx, ∫(x−1)sin(x/4)dx, ∫(2x+3)sin(x/3)dx, ∫(3x−4)sin( x/2)dx, ∫(4x+2)sin(x/5)dx

The solution is in PDF format

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