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Marina56434655442
Marina56434655442
07.11.2021 13:43 •  Алгебра

Спростіть вираз
до ть терміново ​


Спростіть вираздо ть терміново ​

👇
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Ответ:
fhctybq123
fhctybq123
07.11.2021
1  yesterday i had  breakfast at the canteen.  2  last summer we went to the black sea.  3  he didn't call  me last week.  4  why did this girl come to  our office yesterday?   5  when did  you buy tickets last time?   6  last june the boys played  football every morning.  7  on sunday my parents  were at the theatre.  8  i didn't take part at the conference last month.  9  he lived in kiev in his childhood.  10  where did  he send his message?   2 трансформируйте предложения в past simplе  1  he often played chess.  2  our classes began at 9 a. m.  3  she  was always busy.  4  what did you do in the evening?   5  my sister didn’t study at school, she worked at the hospital. 6  my friend prefered tea to coffee.  7  i found many stories in this magazine.  8  he was in my room,  wasn't he?   9  why did you always ask so many questions?   10  jasmine seldom visited her grandparents. 3 образуйте отрицательную форму предложений  1  in summer she didn't get up early.  2  mr. white  didn't write a lot of letters yesterday.  3  on friday they weren't at the station.  4  we didn't  enjoy our time in rome.  5  they didn't  watch a football match last weekend.  6  the girl didn't open a box at once.  7  i didn't leave my keys on the table.  8  the engineer didn't go on business trip on monday.  9  my friend didn't want to move to another flat.  10  i didn't find a surprise in the present-box. 4 поставьте вопросы к предложениям.  1  he learned english at school. (where? what language? why? or …? )  where did he learn english? what language did he learn? why did he learn english? did he learn english or french? 2  the train was five hours late. (what? why? )  what was 5 hours late? why was the train five hours late? 3  i was going to stay at my aunt’s in the crimea. (where? who? or …? ) where was i going to stay in the crimea? who was going to stay at the aunt's in the crimea? was i going to stay at my aunt's or in the hotel in the crimea?   4  they stayed in moscow only for two days. (why? where? how long? ) why did they stay in m only for 2 days? where did they stay? how long did they stay in m?   5  i bought a very beautiful dress in this shop last weekend. (where? what? when? ) where did i buy a very beautiful dress last weekend? what did i buy in this shop last weekend? when did i buy this beautiful dress in the shop? 6  they traveled to cyprus by sea. (how? where? or …? ) how did they travel to c? where did they travel to? did they travel to c or ibiza?   7  i didn’t find your telephone number. (what? why? )  what didn't i find? why didn't i find your telephone number? 8  in his childhood he was always a leader among his friends. (what? when? who? )  what was he in his childhood? when was he a leader among his friends? who was always a leader among his friends in his childhood? 9  he caught a cold last month. (what? when? why? ) what did he catch? when did he catch a cold? why did he catch a cold?   10  we did our lessons together. (what? how? ) what did we do together? how did we do our lessons?
4,4(31 оценок)
Ответ:
Apelsinka32
Apelsinka32
07.11.2021
Метод неопределенных коэффициентов
(2x+1)/[(x-1)^2*(x^2+2x+3)] = A1/(x-1) + A2/(x-1)^2 + (A3*x+A4)/(x^2+2x+3) =
= [A1*(x-1)(x^2+2x+3) + A2*(x^2+2x+3) + (A3*x+A4)(x-1)^2] / [(x-1)^2*(x^2+2x+3)] =
= [A1(x^3+x^2+x-3)+A2(x^2+2x+3)+A3*x(x^2-2x+1)+A4(x^2-2x+1)] /
/ [(x-1)^2*(x^2+2x+3)] =
= [x^3(A1+A3)+x^2(A1+A2-2A3+A4)+x(A1+2A2+A3-2A4)+(-3A1+3A2+A4)] /
/ [(x-1)^2*(x^2+2x+3)] = (2x+1)/[(x-1)^2*(x^2+2x+3)]
Система
{ A1 + A3 = 0
{ A1 + A2 - 2A3 + A4 = 0
{ A1 + 2A2 + A3 - 2A4 = 2
{ -3A1 + 3A2 + A4 = 1

{ A3 = -A1
{ A1 + A2 + 2A1 + A4 = 0
{ 2A2 - 2A4 = 2
{ -3A1 + 3A2 + A4 = 1

{ A3 = -A1
{ A4 = A2 - 1
{ 3A1 + A2 + A2 - 1 = 0
{ -3A1 + 3A2 + A2 - 1 = 1

{ A3 = -A1
{ A4 = A2 - 1
{ 3A1 + 2A2 = 1
{ -3A1 + 4A2 = 2
Складываем 3 и 4 уравнения
6A2 = 3, A2 = 1/2, A4 = 1/2 - 1 = -1/2
3A1 + 2*1/2 = 1, A1 = 0, A3 = 0
Подставляем обратно в интеграл
Int (2x+1)/[(x-1)^2*(x^2+2x+3)] dx = 
= Int [1/2*1/(x-1)^2 - 1/2*1/(x^2+2x+3)] dx =
= 1/2*Int 1/(x-1)^2 dx - 1/2*Int 1/((x+1)^2+2) dx =
= -1/2*1/(x-1) - 1/2*1/sqrt(2)*arctg [(x+1)/sqrt(2)] + C
4,7(4 оценок)
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