Question

Your best submission for each question part is used for your score. 3. [0/1.66 Points] DETAILS PREVIOUS ANSWERS SCALC Evaluate the integral. x2 + x + 1 Jo (x + 1)2(x + 2) boce dx -3 In(3) + 2 In(5) - 4 5 Submit Answer

Answer 1

first find pastial fraction 4 solia x² + xt1 dx + + (X+))?.(x+2) x+1)2(x+2) В (x+1)? x2+x+ 1 = A (x+1)(x+2) + B( X+2) +C (X+1)2 LO 드 X+2 at 1. - ino put 1 = B =) (-1)2+(-1)+41 A(0) + B(-1+ 2) + (10) = put a=-2 in 62)2+(-2)+1 = A (0) + B(0) + (-2+1)2 =c How put B=1, c=3 in o A (x2+ 3x + 2) + (x+2)+3(x+1)2 = x2 (A +3')+ X( 3A+7)+(24+5) equal it A+3= -1 = A=-2 3 x²+x+1 = x2+x +1 above are

-2 . Lt 4 x²+x+1 (X+1) 4*+2) so + Ida 2+1 (x+1)2 x+2 4 -24) -2 In (X+1) + (2+1) - 2+1 + [-2 in 212, +3 In(x+2)] + 3 \n(x+2)] 1 D -2 In [x+1) Xt1 3int-(-2 in 1 + 5 = [2in[5] -(-2. In 1-1+31n2)] = -les in 52+1n73-1-(0-1 +1n2?) S In 7352 +1 -1n2² = N - 4 = In 735² + S १८ اع + 4 S = 0.53941 +4 = ul 5²23 Numeric vale = 1.33941 exact solution is or tu = 3 In (7)- 2 In (5)-3 16(2) +
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