Integrate f(x) = 1/(1-x^2)

1/(1-x2) can be split into the partial fractions A/(1+x) + B/(1-x), where A and B are real constants, which when evaluated by multiplying the equation 1/(1-x2) = A/(1+x) + B/(1-x) through by (1-x2) = (1+x)(1-x) and substituting x =1, and x = -1; we find A = B = 0.5 hence 1/(1-x2) = 1/2(1-x) + 1/2(1+x) which can easily be integrated to 0.5( -log(1-x) + log(1+x)) + c or in the more accepted form 0.5(log(1+x) - log(1-x)) + c. (Where c is a real constant). 

ML
Answered by Mitchell L. Further Mathematics tutor

2715 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Differentiate x = sinhy with respect to x


find general solution to: x(dy/dx) + 2y = 4x^2


Find the inverse of a 3x3 matrix


It is given that f(x)=(x^2 +9x)/((x-1)(x^2 +9)). (i) Express f(x) in partial fractions. (ii) Hence find the integral of f(x) with respect to x.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2026 by IXL Learning