Solved integral of the form ∫(x^2+α)e^(βx)dx

Solved integral of the form ∫(x^2+α)e^(βx)dx

Solution of an indefinite integral of the form ∫(x^2+α)e^(βx)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=2, β=2, α=−3, β=4 is considered; α=3, β=−1; α=−4, β=−2; α=3, β=1;

∫(x^2+α)e^(βx)dx, ∫(x^2+2)e^(2x)dx, ∫(x^2−3)e^(4x)dx, ∫(x^2 +3)e^(−x)dx, ∫(x^2−4)e^(−2x)dx, ∫(x^2+3)e^(x)dx

The solution is in PDF format