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### SOLUTIONS TO INTEGRATION BY PARTS

SOLUTION 10 : Integrate . Let

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

.

Click HERE to return to the list of problems.

Duane Kouba 2000-04-23