.

Now use u-substitution. Let

so that

.

In addition, we can "back substitute" with

.

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

.

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* 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

.

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* 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

.

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* 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

.

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* 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

.

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* 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

=

.

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