Calculus, 9th edition
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The gamma function is , .
Find the values of and .
Substitute in .
.
Substitute in .
.
Substitute in .
.
(b)
Use integration by parts show that .
Substitute in .
Formula for integration by parts :.
Here and .
Consider .
Apply derivative on each side with respect to .
.
Consider .
Integrate on each side.
.
Since .
Therefore, .
(c)
The integral is .
Since .
Therefore, .
(a) , and .
(b) .
(c) .
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