.

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* SOLUTION 2 :* Integrate
. By formula 1 from the introduction to this section on integrating exponential functions and properties of integrals we get that

.

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* SOLUTION 3 :* Integrate
. Use u-substitution. Let

*u* = 7*x*

so that

*du* = 7 *dx* ,

or

(1/7) *du* = *dx* .

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

(Recall that .)

= 4 - 2

= 2 .

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* SOLUTION 4 :* Integrate
. Use u-substitution. Let

*u* = 2*x*+3

so that

*du* = 2 *dx* ,

or

(1/2) *du* = *dx* .

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

(Now use formula 2 from the introduction to this section on integrating exponential functions.)

(Recall that .)

.

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* SOLUTION 5 :* Integrate
. First, multiply the exponential functions together. The result is

(Recall that and .)

(Use the properties of integrals.)

(Use formula 3 from the introduction to this section on integrating exponential functions.)

.

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