Question

English: Solve this integral

PARTIE B: QUESTIONS À DÉVELOPPEMENT : Question 10. [5 points) Calculer l'intégrale indéfinie suivante.

Answer 1

We evaluate the value of the given indefinite integral by using partial fraction decomposition method.
Given infegral l 23 + n du 2-2011 : Now = 2(x+") du partial fraction decomposition method . using seta (x) ant at a lat) + Manga a m(antu) n(n+1)*+A(x+1)*+ B(n-1) + : (-1) (-1) 7 montu) = n(n-1) +A(n-1) "+B(14) + ... put a=1 in U and get . . !(+1) = 1 (1-1) +A(1-1)*+B(1-1) tc 7 23:0 tot orc 1. e=2 را)

Again put neo in U and get 0 (04+0) =0(0-1)"+ A (0-1)+ B(0-1)+c a o'z 0+ A -B'+ 2 [::(=2] .* . B-A22 .. (2) again put na 2 in () and get 2(2+2) = 2(2-1)2 +A(24)*+B12-1) + e 3 12 = 2 (1) + A +B(1) + 2 [:c22] 1222 +A+B+ 2 . 7. 12-4 - AtB =) At Ba 8 - (3) - solving (2) and (3). and get B-A=2 from (3) we get BtA=8 . Az 8-B Adding 2B 210 7 B=5 = 5 don Finally, we get Az 3, B 5 , c?.2

ubito Therefore the given infegral can be written a sering dan floring treating de In + A+ m 3nt Ju du + 3 aut sfat, da tz ingatan - * +32 +5112-1| +2 (wvj*du a monta 34 +5 62+1 +2 (47)*t! te > * +34 +51010-1| +2 (24)"+c = m + 3x +5 in/a-11 - 2 te .+ 3n. -2 +1 CX - 22+1