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). 

Related Further Mathematics A Level answers

All answers ▸

Differentiate w.r.t x the expression arccos(x).


z = 4 /(1+ i) Find, in the form a + i b where a, b belong to R, (a) z, (b) z^2. Given that z is a complex root of the quadratic equation x^2 + px + q = 0, where p and q are real integers, (c) find the value of p and the value of q.


Solve x^2+8x-5=0 using completing the square


How do you deal with 3 simultaneous equations? (Struggling with Q7 of AQA specimen paper 1)


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2024

Terms & Conditions|Privacy Policy