*u* = *x*^{2}+5*x*

so that

*du* = (2*x*+5) *dx* .

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

.

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* SOLUTION 2 :* Integrate
. Let

*u* = 3-*x*

so that

*du* = (-1) *dx* ,

or

(-1) *du* = *dx* .

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

.

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* SOLUTION 3 :* Integrate
. Let

*u* = 7*x*+9

so that

*du* = 7 *dx* ,

or

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

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

.

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* SOLUTION 4 :* Integrate
. Let

*u* = 1+*x*^{4}

so that

*du* = 4*x*^{3} *dx* ,

or

(1/4) *du* = *x*^{3} *dx* .

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

(Do not make the following VERY COMMON MISTAKE : . Why is this INCORRECT ?)

.

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* SOLUTION 5 :* Integrate
. Let

*u* = 5*x*+2

so that

*du* = 5 *dx* ,

or

(1/5) *du* = *dx* .

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

.

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* SOLUTION 6 :* Integrate
. Let

*u* = 3*x*

so that

*du* = 3 *dx* ,

or

(1/3) *du* = *dx* .

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

.

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* SOLUTION 7 :* Integrate
. Let

so that

.

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

.

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