How do you integrate by parts?

Using the formula (given in the formula booklet):∫ u(dv/dx) dx = uv − ∫ v(du/dx) dxFor example if we want to integrate ∫xsin(x) we can take x to be u and sin(x) to be (dv/dx).So ∫ xsin(x) dx = x(-cos(x)) − ∫ -cos(x) dx = -xcos(x) + sin(x) + cFor integration by parts with multiple steps I like to use the DI method which requires drawing a table.Integrals with both e^x and either sin or cos in them require a different procedure involving both the DI method and basic algebra.