Question

u want to use integration by parts to find J (5.x - 7) (x - 1) 4 dx, which is the better choice for u: U = 5x – 7 or u = (x - 1) 4? Explain your choice and then integrate. B blems 15–28 are mixed—some require integration by parts, others can be solved with techniques considered earlier. ntegrate as indicated, assuming x > 0 whenever the natural logarithm function is involved. 15. ( xe* ax 16. S (x - 1)e* de 17. to do

please solve 21 and 25 only

Answer 1

Solution:

21.

21 s In (2x) dx In (2x). I da let Sav=Si.doc let u = ln (2x) da V=x Sudr = uv-sudu - Inc2x). - ( 3.)dx) x In (2x) - J da x In (2x) - x )dx= x ln(2x) - a to [ (xlmax-x)+c] aln(b) a In (6") • Ince")alnce) = {3 \n(6) – 3 +c] - [1.In(2) -1 +c] 3 3 1n(6) -3 - In (2) + 1 = el a In (6?) - In (2) -2 = 1n (63) -2 = ln (108) - 2 = In (108) -In (e?) In(108) - SIN( 23 )da In (2x) da

Hence, integration value we get is .

In2ädt = In(108

25.

25. J In (x) dx x let u = ln(x) au = I doc = utc = (ln(x))" + c

Hence, integration value is given by, .

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