and

so that

and .

Therefore,

.

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* SOLUTION 11 :* Integrate
. Let

and

so that

and .

Therefore,

.

Use integration by parts again. Let

and

so that

and .

Hence,

.

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* SOLUTION 12 :* Integrate
. Let

ein and

so that

and .

Therefore,

.

Use integration by parts again. Let

and

so that

and .

Therefore,

.

Use integration by parts for a third time. Let

and

so that

and .

Hence,

.

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* SOLUTION 13 :* Integrate
. Let

and

so that

and .

Therefore,

.

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* SOLUTION 14 :* Integrate
. Let

and

so that

and .

Therefore,

.

Now use the trig identity

,

getting

.

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* SOLUTION 15 :* Integrate
. Let

and

so that

and .

Therefore,

.

Use integration by parts again. Let

and

so that

and .

Hence

.

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Duane Kouba 2000-04-23