SOLUTION 17 : Integrate . First factor the denominator, getting

.

Now use u-substitution. Let

so that

.

In addition, we can "back substitute" with

.

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

.

SOLUTION 18 : Integrate . First complete the square in the denominator, getting

.

Now use u-substitution. Let

so that

.

In addition, we can "back substitute" with

.

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

.

In the first integral use substitution. Let

so that

,

or

.

Substitute into the first integral, replacing all forms of , and use formula 3 from the beginning of this section on the second integral, getting

.

SOLUTION 19 : Integrate . First factor out a 2 and complete the square in the denominator, getting

.

Now use u-substitution. Let

so that

.

In addition, we can "back substitute" with

.

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

.

In the first integral use substitution. Let

so that

,

or

.

Substitute into the first integral, replacing all forms of , and use formula 3 from the beginning of this section on the second integral, getting

.

SOLUTION 20 : Integrate . First rewrite this rational function by multiplying by , getting

(Recall that .)

.

Now use substitution. Let

so that

,

or

.

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

.

SOLUTION 21 : Integrate . Use u-substitution. Let

so that

.

Now rewrite this rational function using rules of exponents. Then

.

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

.

SOLUTION 22 : Integrate . First rewrite this rational function as

.

Now use u-substitution. Let

.

so that

,

or

.

In addition, we can "back substitute" with

.

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

=

.