Here the column at the left contains the successive derivatives of u(x). The
column at the right contains the successive antiderivatives of v(x) (always with C
= 0); that is, v 1 (x) is the antiderivative of v(x), v 2 (x) is the antiderivative of v 1 (x),
and so on. The diagonal arrows join the pairs of factors whose products form the
successive terms of the desired integral; above each arrow is the sign of that
term. By the tic-tac-toe method,
BC ONLYExample 47 __
To integrate x^4 cos x dx by the tic-tac-toe method, we let u(x) = x^4 and v(x) =
cos x, and get the following table:
The method yields