Integral of (2(x^3)-7)/((x^4)-14x)

Set f(x)= (x^4)-14x. f’(x)=4(x^3)-14=2(2(x^3)-7). Thus we can write (2(x^3)-7)/((x^4)-14x)=(1/2)f’(x)/f(x). The integral of f’(x)/f(x)=ln|f(x)|+c. Thus the integral of (2(x^3)-7)/((x^4)-14x) is (1/2)(ln|f(x)|+c)=(1/2)ln|(x^4)-14x|+C.

Answered by Issy K. Maths tutor

2801 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The curve C has the equation y = 1/2x^3 - 9x^3/2 + 8/x + 30, find dy/dx. Show that point P(4, -8) lies on C


Using implicit differentiation, write the expression "3y^2 = 4x^3 + x" in terms of "dy/dx"


What are the advantages of using numerical integration (Trapezium rule, Simpson's rule and so on) over direct integration?


What is differentiation and how is it used?


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 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences