Solving an indefinite integral of the form ∫(αx+β)sinγxdx 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=−1, γ=2 is considered; α=1, β=4, γ=3; α=4, β=−2, γ=4; α=2, β=4, γ=1;

∫(αx+β)sinγxdx, ∫(3x−1)sin2xdx, ∫(x+4)sin3xdx, ∫(4x−2)sin4xdx, ∫(2x+4)sinxdx

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