need a substitution for integral?

Question

help me find a sub in order to integrate
x^4(1-x)^4/(x^2-1)

sorry, the denominator is (x^2+1), kinda changes this

Answer 1

Do (x^2-1)=(x+1)(x-1)= -(1-x)(x+1)
After simplify you´ll get
x^4(x^3-3x^2+3x-1)/(x+1)
it's OK?
If not be free to email

OK, after the change my tip is:
remember that derivative of arctan(x)=1/(x^2+1) and will be fine. Good luck. Call me if you need.

Answer 2

Since x^2 - 1 = (x -1)(x +1), for every x <>1, we have (x^4(1-x)^4)/(x^2-1) = (x^4(x-1)^3)/(x + 1). The solution requires some algebraic work, so I won't get into the details, but will give you the directions. You multiply x^4 by (x -1)^3 = x^3 - 3x^2 + 3x -1 and gets x^7 - 3 x^6 + 3x^5 - x^4. Then, you use the division algorithm to dived this 7 degree polynomial by the binomial x +1. The division is not exact, so that x^7 - 3 x^6 + 3x^5 - 3x^4 = (x+1) P(x) - 8. where P is a polynomial of degree 6. I know the remainder is -8 because the remainder is the value of x^4 (x -1)^3 for x = -1.
Therefore, we have to integrate ((x+1) P(x) - 8)/(x +1) = P(x) - 8/(x+1). Integratin the polynomial P is kinda easy, right? It's anotehr polynomial Q of degree 7. And integrating 8/(x+1) is kinda easy too, we get 8 ln(x+1). So, our integral is Q(x) + ln(x+1). The integration constant is included in the independednt term of Q.
If you need more help, just email me

Answer 3

im not sure if i could even answer this, but i think i could, i just dont have the time, is this algebra or calculas? hey your spending the time to try and get it right, thats good, but, a math book should have the answer, or an explination on how to figure it out, to figure out this answer is not as important as being able to learn the textbook. but, i think the reason why they make us do all the math questions is cuz, 5x5=25 and 2x7 = 14 and these are no brainers and your question should be a no brainer and it will be if you do your homework. too bad they never thought me that in school, that their stupid assignments would actually help me, all they did was burden me, and what kind of teacher cant get that message thru? what teacher could