How do you integrate x/(1+x^4)? Calculus Introduction to Integration Integrals of Rational Functions 1 Answer Antoine May 5, 2015 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 = 1/2arctan(x^2) Answer link Related questions How do you integrate (x+1)/(x^2+2x+1)? How do you integrate dx / (2sqrt(x) + 2x? What is the integration of 1/x? How do you integrate (1+x)/(1-x)? How do you integrate (2x^3-3x^2+x+1)/(-2x+1)? How do you find integral of ((secxtanx)/(secx-1))dx? How do you integrate (6x^5 -2x^4 + 3x^3 + x^2 - x-2)/x^3? How do you integrate ((4x^2-1)^2)/x^3dx ? How do you integrate (x+3) / sqrt(x) dx? How do you find the integral of (x^4+x-4) / (x^2+2)? See all questions in Integrals of Rational Functions Impact of this question 6821 views around the world You can reuse this answer Creative Commons License