Integrate the following fraction w.r.t. x: (sqrt(x^2 + 1)-sqrt(x^2 - 1))/(sqrt(x^4 - 1))

Notice the denominator can be factorised as the difference of two squares. The fraction can then be simplified by cancellation. The resulting fraction(s) can then be solved using the list of integrals in your formulae and tables book. The final answer: ln|x+sqrt(x+1)| - ln|x+sqrt(x-1)| + C, |x|>1. (I hope to further explain the steps taken to solve this question using the whiteboard!)

TD
Answered by Tutor80072 D. Maths tutor

4582 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A geometric progression has first term 3 and second term -6. State the value of the common ratio.


Find the differential of y(x)=(5x*Cos(3x))^2


Express 3cos(x)+4sin(x) in the form Rsin(x+y) where you should explicitly determine R and y.


f(x)= 2x^3 -7x^2 + 2x +3. Given that (x-3) is a factor of f(x), express f(x) in a fully factorised form.


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