Question

Can someone write the steps on solving this with integration? Exam based on this equation.

Зr +7 '(x-1)*(x? +4)

Answer 1

To evaluate : r 34+7 - du Ja-1? (274) First we break the integrand into partial fractions: 34+7 Let +B + Cuts (2-13 (4+4) (4-112 274. AM (4-12 (4+4) Sut? A(-1)(x+4) + 3C4+4) + (n+D) (4-12 01-15 (2574) 34+7= A(WP-2 +42-4) + Bx +4) + (Cu+D) cn=24+) 34+7 = (A+) x + (-A+B-2C+D) x' +(4A+8–2D) x+ (-4A+48 +D) comparing the coefficients Atc=0 -- -- - A+B-2C+D=0.-(1) 4A + (-2D=3. -- GID -4A +4B+D=7.- (iv). from lis A=-( putting this value of Ain (i), (ii), (iv). (+B-2C+D=0) B-CHD=0 ---(V). -4C+ (-2D=] , -3(-2D -- 3 -- (VI) 44+4B*D= 7 4 3 +4 CHD=7 - VID. by the operation (vii) - 4x(v) 43+4C+ D=7 43-46 +4D=0 8C-3D=7 lix) multiplying (vi) by 3, (ix) by 2, then subtracting -9C-6D=9 16C-60= 14 -250 -5 22% +

vil putting this value of c in 2D=) >> 203-3-3 » 2011 » De A2-C 2-2 from v Be-D 5-6 -5 + 2 - روبشی آر - - - - 1914 sastaget a + "34+7 dn 015 (444) + 12-12 --dx + 2 Sky2du+ FS hartu du - Soutte du -- le(x-1) +2. (1-10 Mura)-2. & tants - lan-1)- to lase +41-2 tant (2) te In the third integral, but 174=t 32nduzdt Sudnede Shende Softwa) le (144) In the fourth integral Strane Sneezda = 4