SOLUTION 1 : Integrate . First, split this rational function into two parts. Thus,

(Now use formula 1 from the introduction to this section.)

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SOLUTION 2 : Integrate . Use u-substitution. Let

so that

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

(Now use formula 1 from the introduction to this section.)

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SOLUTION 3 : Integrate . Rewrite the function and use formula 3 from the introduction to this section. Then

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SOLUTION 4 : Integrate . Use u-substitution. Let

so that

,

or

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

(Now use formula 1 from the introduction to this section.)

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SOLUTION 5 : Integrate . First, use polynomial division to divide by . The result is

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In the second integral, use u-substitution. Let

so that

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

(Now use formula 1 from the introduction to this section.)

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SOLUTION 6 : Integrate . First, use polynomial division to divide by . The result is

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In the third integral, use u-substitution. Let

so that

,

or

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For the second integral, use formula 2 from the introduction to this section. In the third integral substitute into the original problem, replacing all forms of , getting

(Now use formula 1 from the introduction to this section.)

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SOLUTION 7 : Integrate . Use u-substitution. Let

so that

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

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

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SOLUTION 8 : Integrate . Use u-substitution. Let

so that

.

In addition, we can "back substitute" with

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

(Combine and since is an arbitrary constant.)

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