Question

Find intergral
(x-1)^2 / x^4

Answer 1

do u know the basic integration formula for x^n ?

Answer 2

hint : expand (x-1)^2 first

Answer 3

kind of.. my book doesnt have example of this type of question..

Answer 4

my room substitute x-1 as u, then u^2

Answer 5

so what is \(\huge \int x^ndx\)
you can solve this easily without substitution

Answer 6

that's just x^n+1 / n+1

Answer 7

correct.
so first expand the numerator, (x-1)^2
what u get?

Answer 8

(x-1)^3 / 3 + C ?

Answer 9

no no, i asked you to expand , not integrate.

Answer 10

u mean x^2 - 2x+ 1？

Answer 11

and actually that integration is wrong lol.. forgot something

Answer 12

right, now divide x^4 to each of the 3 terms, what u get ?

Answer 13

ohh,

Answer 14

what did u forget ?

Answer 15

1/ x^2 - 2/x^3 +1/x^4

Answer 16

oh nvm...that one is right

Answer 17

yeah, 1/ x^2 - 2/x^3 +1/x^4 is correct, now integrate each term separately usin integral of x^n

Answer 18

ohh ok i get it. thanks, that's really helpful.
for 1/x^2, it's just x^-2, and then do the same thing right

Answer 19

correct :)
welcome ^_^