Page 39 - Calculus for the Clueless, Calc II

Note the nice pattern of the coefficients and the exponents of this answer. Well, I like it!

Example 26—

This integral can be done in two new ways, both of which are useful.

Method A

Let u = the whole radical.

2
2
1/2
2
u = (x + 4) ; u = u + 4; x = u - 4; 2x dx = 2u du; or x dx = u du. Substituting,
2
2

Method B

Let v = what's under the radical sign.

v = x + 4; x = v - 4; and 2x dx = dv. Substituting,
2
2