Question

- Calculate I (x-1)² -oo (x² + 4x+8) ² dx

Answer 1

f (x-17² dx ao C2392+8) tix Let 6x) = 6L-132 of 9(x) = (x?+4x+8)2 P & as As gle) can be differentiate in two repeated roots kau is a Bropeu fredion gin) gou) Ston) can be written as fies) + (1261) de 8. x) go (ve) As g61) = (x²+42 +82 igion = 9261) = (x +4x+8) 4 9'60)= 262?+up+8) (2x+4) = f,95.0 = 5x134 & 326) = 13 ... The equation is can be modified as 5x+34 + 8(x²+42+8) (13 dx J8(x² +42+8) 11). Solving is de & putting in ean. ii) 8 (x²+4x+8)

dx =3 da J8x²+42+8) 8 Ja²+uat8 (ar 13 l dx llo: (x 80x²+2.22 +2²+4 sl (c) & Bl de ily 8 + 2)² + 4 x (N) oo cool at2 = a Let s dx+2 = 2a = doc= ada 8+300 8+ - . ) 00 0- 2009 A Putting these value in ean. Irix we get 132 dat 13 l da 16 at 1 = 13 tanical Putting value of x again we get 13 tan" (at2)

Putting this value ean. lid we get 5x+34 + 13 tan(at2) +Clu 8(x² + 4x+8) 16 I ator lots oder nut as a strollib sooroo OOR Putting the limit in the solution we get at 5x +34 + 13 tan (2+2) 10 | 8 61? +4248) 16 ex ot B T = 13 T $18+ ) 05 AL