2018年4月8日 · (x-1)^4 -= x^4 -4 x^3 + 6x^2- 4x+1 We can expand the expression using the binomial theorem: (x-1)^4 -= sum_(r=0)^4 ( (n), (r) ) (x)^r(-1)^(n-r) " " = ( (4), (0) ) (x ...

2018年5月2日 · x^4+4x^3+6x^2+4x+1 The binomial theorem states: (a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4 so here, a=x and b=1 We get: (x+1)^4 = x^4+4x^3(1)+6x^2(1)^2+4x(1)^3+(1)^4 (x+1)^4 = x^4+4x^3+6x^2+4x+1

2016年9月24日 · 64557 views around the world You can reuse this answer ...

2017年9月18日 · I = int_(-oo)^(oo) 1/(1+x^4) \\ dx = (pisqrt(2))/2 Sorry that this is such a long solution: We seek: I = int_(-oo)^(oo) 1/(1+x^4) \\ dx graph{1/(1+x^4) [-5, 5, -2.5, 2.5]} The function is well defined over the domain RR. In order to compute this definite integral, consider the following complex variable function over a domain CC: f(z) =1/(1+z^4) And its associated …

2017年10月3日 · The answer is long, so please see the below. Key points are factorization, finding coefficients of an identity, integration of (f'(x))/(f(x)) and 1/((x+p)^2+q). x^4+1 is not able to be factorized in rationals. However, like x^4+4=(x^2+2)^2-(2x)^2=(x^2+2x+2)(x^2-2x+2), you can factorize x^4+1 in reals: x^4+1=(x^2+1)^2-(sqrt(2)x)^2=(x^2+sqrt(2)x+1)(x^2-sqrt(2)x+1) Note …

2018年4月18日 · x^4-1=(x^2+1)(x+1)(x-1) using complex numbers x^4-1=(x+ib)(x-ib)(x+1)(x-1) we make use of the difference of squares a^2-b^2=(a+b)(a-b) x^4-1=(x^2+1)(x^2-1) we can use dos for the second bracket once more x^4-1=(x^2+1)(x+1)(x-1)--(1) for real numbers we can proceed no further, but if we use complex numbers note" "i^2=-1 we see a^2+b^2=a^2-(ib)^2=(a+ib)(a …

2015年5月5日 · int x/(1+x^4)dx =1/2arctan(x^2) Method int x/(1+x^4)dx = 1/2int (2xdx)/(1+(x^2)^2)=1/2int (d(x^2))/(1+(x^2)^2) ="I" let x^2 =u =>"I"= 1/2int (du)/(1+u^2) = 1/2arctanu ...

2010年1月22日 · I am trying to factor x 4 +1 into two multiplied polynomials Homework Equations My teacher gave us this hint that its factored form is (ax2+bx+c)(ax2+bx+c) The Attempt at a Solution First i assumed that a and c were equal to 1 so that when x 2 is multiplied by the other x 2 is gives me x 4 and 1 times 1 gives me 1. I knew that b had to be a ...

2015年5月19日 · One law of exponent states that a^-n=1/a^n. In this case, 1/x^-4=(x^-4)^-1 But another law of exponent states that (a^n)^m=a^(n*m) Thus, (x^-4)^-1=x^((-4)(-1))=x^4 Finally, 1/x^-4=x^4

2016年12月12日 · -4/x^5 d/dx(1/x^4) = d/dx(x^-4) Applying the power rule: d/dx(1/x^4) =-4* x^-5 =-4/x^5