I am stuck on this integration by parts problem. #2u=Ixlux dx3×dv=lnx dxv=x/nx-xdu = 3 dx= ( + x) (x Mx-x) - ((^~^l^x-~^~) =:Inx-x)3= 1/2 x (x²^x-x) - S 3x²₁x - 32 x dxDistributedx(px & Day + FS-5²-4₁² ²2x- 1/2 x (x/ax-x) - S 13x/nx - x - 1 x² +C

Using Integration By-parts formula

#2 du = Ixlux dx 3 13 x 3 dx dv=lnx dx V= x/nx-x Distribute clnx-x). = (1+x) (x I^x-x) - √(x^²^x-x^²) = de dx = 1² x (x/x-x) - S 3x²₁x- £x dx ix/nx = 1/2 X(XM-x) - √ £ x 1x²x- (S = = -1/2 x (x/ax-x) - S 13x/²x-x - £ x² +C хавх

#2 du = Ixlux dx 3 13 x 3 dx dv=lnx dx V= x/nx-x Distribute clnx-x). = (1+x) (x I^x-x) - √(x^²^x-x^²) = de dx = 1² x (x/x-x) - S 3x²₁x- £x dx ix/nx = 1/2 X(XM-x) - √ £ x 1x²x- (S = = -1/2 x (x/ax-x) - S 13x/²x-x - £ x² +C хавх

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...

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Question

I am stuck on this integration by parts problem.

#2
u=
Ixlux dx
3
×
dv=lnx dx
v=x/nx-x
du = 3 dx
= ( + x) (x Mx-x) - ((^~^l^x-~^~) =
:Inx-x)
3
= 1/2 x (x²^x-x) - S 3x²₁x - 32 x dx
Distribute
dx
(px & Day + FS-5²-4₁² ²
2
x
- 1/2 x (x/ax-x) - S 13x/nx - x - 1 x² +C

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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