Question

Evaluate the following integrals. Integral x*ln(x^2+3x+2)dx

2. (8 points) Evaluate the following integrals. Answers without supporting work will re- ceive no credit. (a) (5 points) | < ln(x2 + 3x + 2) dx

Answer 1

2) a) Solm. Now, ali (x²+30+2) := winlfa+i) (0+2)) = nellm (x+1] + ln (+2)) = xm (+1) + xln (0+2) Therefore, Jam(x²+3x+2) da = beln (a +1) + xil n(22+27) dx = J bein(x+3) dx + fain(x+2) dx -0 Now Salm (+1) dx , Et In +1) 5 x Doe - On (2+100 sadnjdx = 22 m (+1) - Siti 22 de 22 in (*+1) 1/2 l (22²_17+1 da. a m (at) - I. I peti) (x-1) +1 dae = (+1) - 8 -1) + ) * = (4+19 - - x +\n\x+11) +9 A co be the constant of - bez 641) - ter in i integration. in (x+1) - + Patel 7 +1 . : 20+1

and Jan (2+2) dx = 10(+2) Sadri -Stem (In (427) Sve du] du :- 22 m (2+2) - 1 eta 22 da - 22 /n (1x + 2) - 12 / (x2 - 1) + 4 dn = x2 In (2e +2) - + |(60+ 2) (442) + un de = ² m ( x + 2) - 22 J Gr + 2) dx = 28 de az 12 m2 in (x+2) – 1 (+23) – 2\n<« «2) T ty where ea is the constant of . integration ... = Me -2) Iné2+2) – mot using these in o, we have Jumla2+3x+2) dx = 1921) en (oct 1) - 2 + 1 te +(2-2) in (1+2) - = 1013m(x+1) +(229)imente) - - 2 +e, where [e= 4+6) +₂