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|.

Answered by Tutor22645 D. Maths tutor

3974 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How would you show that a vector is normal to a plane in 3D space?


What is the indefinite integral ∫5exp(3-4x)dx ?


Express 3 cos θ + 4 sin θ in the form R cos(θ – α), where R and α are constants, R > 0 and 0 < α < 90°.


Find the tangent to the curve y=(3/4)x^2 -4x^(1/2) +7 at x=4, expressing it in the form ax+by+c=0.


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