Solving an indefinite integral of the form ∫(x^2+α)sinβxdx 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=1, α=1, β=2 is considered; α=−5, β=3; α=3, β=4

∫(x^2+α)sinβxdx, ∫(x^2−2)sinxdx, ∫(x^2+1)sin2xdx, ∫(x^2−5)sin3xdx, ∫(x^2+3)sin4xdx

The solution is in PDF format