### SOLUTIONS TO U-SUBSTITUTION

SOLUTION 14 : Integrate . Let

u = 4-x

so that

du = (-1) dx ,

or

(-1) du = dx .

In addition, we can "back substitute" with

x = 4-u .

Substitute into the original problem, replacing all forms of x, getting

.

SOLUTION 15 : Integrate . Let

u = 2x+3

so that

du = 2 dx ,

or

(1/2) du = dx .

In addition, we can "back substitute" with

x = (1/2)(u-3) .

Substitute into the original problem, replacing all forms of x, getting

.

SOLUTION 16 : Integrate . Let

u = x+2

so that

du = (1) dx = dx .

In addition, we can "back substitute" with

x = u-2 .

Substitute into the original problem, replacing all forms of x, getting

.

SOLUTION 17 : Integrate . Let

so that

.

In addition, we can "back substitute" with

.

Substitute into the original problem, replacing all forms of x, getting

.

SOLUTION 18 : Integrate . Let

.

In addition, we can "back substitute" with

,

or

x = (4-u)2 = u2-8u+16 .

Then

dx = (2u-8) du .

In addition, the range of x-values is

,

so that the range of u-values is

,

or

.

Substitute into the original problem, replacing all forms of x, getting

.