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

∫(αx+β)e^(γx)dx, ∫(x−1)e^(2x)dx, ∫(2x+3)e^(3x)dx, ∫(3x−4)e^(−2x )dx, ∫(4x+2)e^(−3x)dx, ∫(−2x+2)e^(−3x)dx, ∫(−3x−2)e^(4x)dx

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