Let m and n be positive integers and a+ 0. Using partial integrals, show that 1 "" dz = 2="c** - "/2-" dz, „n-1̟ar dx, a a am+1 -(In z)" т+1 n | 2" (In z)" dr: 1" (In z)"-1 d.x. %3D т+1 then use the reduction formula to determine (a) ³ e²² dx,

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Let m and n be positive integers and a+ 0. Using partial integrals, show that
1
x"eª* dx = -x"eª*
x"-'ea dx,
ar
a
a
m+1
-(In z)"
m +1
-/z" (In z)"-1 dz.
a" (ln x)" dx
%3D
т+1
then use the reduction formula to determine
(a)
1³ e2= dx,
(b) / x²(Inz)³ dzr.
Transcribed Image Text:Let m and n be positive integers and a+ 0. Using partial integrals, show that 1 x"eª* dx = -x"eª* x"-'ea dx, ar a a m+1 -(In z)" m +1 -/z" (In z)"-1 dz. a" (ln x)" dx %3D т+1 then use the reduction formula to determine (a) 1³ e2= dx, (b) / x²(Inz)³ dzr.
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