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

3872 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Can you explain the product rule when differentiating?


Solve ∫(x+2)/(2x^2+1)^3 dx


Polynomial long division, how do I do it?


Find the two real roots of the equation x^4 - 5 = 4x^2 . Give the roots in an exact form. [4]


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo
Cookie Preferences