Page 34 - Calc for the Clueless

Example 29—

Here's a tricky one.

Let u = x - 1. x = 1; u = 0. x = 2; u = 3. dx = du/2x.
2

Note

If you make a u substitution and the x's do not cancel out, either a new technique must be used or the problem
cannot be solved.

Example 30—

Let u = 5x. dx = du/5.

The integral of the sine is minus cosine and the integral of the cosine is the sine.

You must replace u with 5x since the problem originally had x.

Note

You must know how to do an integral like this one by sight, because if you don't, some of the calc II integrals
will become virtually endless.

Example 31—