Barrons AP Calculus

and dv = exdx so that du = dx and v = ex. Thus,

.

Example 45 __

Find .

SOLUTION: To integrate, we can let u = ex and dv = cos x dx; then du = exdx, v
= sin x. Thus,

.

BC  ONLY

To evaluate the integral on the right, again we let u = ex, dv = sin x dx, so that du
= exdx and v = −cos x. Then,

Example 46 __

Find ln x dx.

SOLUTION: We let u = ln x and dv = x^4 dx. Then, du = dx and . Thus,

.

The Tic-Tac-Toe Method^1

This method of integrating is extremely useful when repeated integration by
parts is necessary. To integrate u(x)v(x) dx, we construct a table as follows: