A method of integration
which can be considerably easier than integration by parts
. In order to use tabular integration
, one "part" of the integral must be a polynomial
. Set up a table in such a manner that you have the polynomial in one column and the rest of the integral in the other. Differentiate the polynomial until your derivative is equal to zero. For every time you differentiate, integrate the rest of the former integral. This is easier to demonstrate with an example, so... let's go.
S x^2*cosx dx
Now it's a game of draw the lines. Draw a line from x^2 to sinx, then a line from 2x to -cosx, then a line from 2 to -sinx. Now that you've got that visualized, it's a fairly easy process. Simply multiply the two terms together that you have connected by the line. Now, for the first line you drew, the product is to be added to the total. For the second line, the product is to be subtracted. For the third, it is to be added. For all successive lines drawn, the same pattern is continued.
x^2*sinx - (2x*-cosx) + (2*-sinx) = x^2*sinx + 2x*cosx - 2*sinx + C is the integral. This technique is especially useful for when multiple applications of the integration by parts method are needed to yield an answer.