(In the denominator use trig identity A from the beginning of this section.)

(Use antiderivative rule 5 and trig identity F from the beginning of this section.) truein

.

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* SOLUTION 11 :* Integrate
. First square the function, getting
truein

(Use trig identity G from the beginning of this section.)

.

Now use u-substitution. Let

so that

,

or

.

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

(Use antiderivative rule 4 on the first integral. Use antiderivative rule 6 on the second integral.)

(Combine constant with since is an arbitrary constant.)

.

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* SOLUTION 12 :* Integrate
. Use u-substitution. Let

so that

.

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

.

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* SOLUTION 13 :* Integrate
. First rewrite the function (Recall that
.), getting

(Now use trig identity F from the beginning of this section.)

.

On the first integral use u-substitution. Rewrite the second integral and use trig identity F again. Let

so that

.

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

.

Use u-substitution on the first integral. Use antiderivative rule 7 on the second integral. Let

so that

.

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

.

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* SOLUTION 14 :* Integrate
. Use u-substitution. Let

so that

,

or

.

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

.

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* SOLUTION 15 :* Integrate
. Let

so that

.

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

.

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* SOLUTION 16 :* Integrate
. (Hello ! The term
is NOT the product of and . It is the functional composition of functions and . ) Use u-substitution. Let

so that

,

or

.

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

.

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* SOLUTION 17 :* Integrate
. Use u-substitution. Let

so that

.

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

.

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* SOLUTION 18 :* Integrate
. Use u-substitution. Let

so that

,

or

.

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

.

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