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.

IK
Answered by Issy K. Maths tutor

2993 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

differentiate: y^2 + 3xy + x + y = 8


How can I differentiate x^2+2y=y^2+4 with respect to x?


Find two positive numbers whose sum is 100 and whose product is a maximum.


How can functions be transformed?


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences