find the definite integral between limits 1 and 2 of (4x^3+1)/(x^4+x) with respect to x

first notice the integral is in the form f'(x)/f(x), and indefinite integrals of this form are ln|f(x)|+c.
therefore the integral is [ln|x4+x|] between limits 1 and 2.
subbing in limits gives ln|24+2|-ln|14+1|
simplifying gives ln|18|-ln|2|
and by log rules this is equivalent to ln|18/2|=ln|9|.

TD
Answered by Tutor22645 D. Maths tutor

4023 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the derivative of the following function with respect to x. y = 5e^x−2xsin(x)


integral of xe^-x dx


Differentiate 3x^2+1/x and find the x coordinate of the stationary point of the curve of y=3x^2+1/x


The curve C has equation y = x^3 - 3x^2 - 9x + 14. Find the co-ordinates and nature of each of the stationery points of C.


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