SOLUTION 9 : Integrate . First, complete the square in the denominator. The result is

.

Now use u-substitution. Let

so that

.

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

(Use formula 2 from the introduction to this section.)

.

SOLUTION 10 : Integrate . First, factor 2 from the denominator. The result is

(Complete the square in the denominator.)

.

Use u-substitution. Let

so that

.

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

(Use formula 3 from the introduction to this section.)

.

SOLUTION 11 : Integrate . Because of the term in the denominator, rewrite the term in a somewhat unusual way. The result is

.

Now use u-substitution. Let

so that

,

or

.

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

(Use formula 3 from the introduction to this section.)

.

SOLUTION 12 : Integrate . Use u-substitution. Let

so that (Don't forget to use the chain rule on .)

,

or

.

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

(Use formula 1 from the introduction to this section.)

.

SOLUTION 13 : Integrate . First, rewrite the denominator of the function, getting

.

Now use u-substitution. Let

so that

.

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

(Use formula 2 from the introduction to this section.)

.

SOLUTION 14 : Integrate . Use u-substitution. Let

so that (Don't forget to use the chain rule on .)

,

or

.

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

(Use formula 1 from the introduction to this section.)

.

SOLUTION 15 : Integrate . First, rewrite the denominator of the function, getting (Recall that .)

.

Now use u-substitution. Let

so that

.

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

(Use formula 2 from the introduction to this section.)

.

SOLUTION 16 : Integrate . Use u-substitution. Let

so that

,

or

.

In addition, we can "back substitute" with

.

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

(Combine and since is an arbitrary constant.)

.