*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

.

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* SOLUTION 15 :* Integrate
. Let

*u* = 2*x*+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

.

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* 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

.

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* SOLUTION 17 :* Integrate
. Let

so that

.

In addition, we can "back substitute" with

.

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

.

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* SOLUTION 18 :* Integrate
. Let

.

In addition, we can "back substitute" with

,

or

*x* = (4-*u*)^{2} = *u*^{2}-8*u*+16 .

Then

*dx* = (2*u*-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

.

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