Answers>Maths>IB>Article

Integrate x^3 * lnx

I would start by asking the student the different forms of integration we know (e.g. substitution, parts).I would then ask the student whether parts or substitution gives the easiest method.If the student isn't sure which method to use, I would ask them to try substitution first so that they can see that substitution doesn't lead to a simplification of the problem.
Integration by parts formula: ∫ u(dv/dx) dx = uv − ∫ v(du/dx) dxIf the student is unsure about which term (x3 and lnx) to use for u and v, I would ask them to consider which term is difficult to integrate and easy to differentiate. This should lead them to u = lnx and dv/dx = x3.
u = lnx dv/dx = x3 du/dx = 1/x v = x4/4
Then simply substitute the values u, v, du/dx, dv/dx into the parts formula to solve for the answer.
(x4/4lnx) - 1/4∫x3 = (x4/4lnx) - x4/16 + C

AA
Answered by Arjun A. Maths tutor

3011 Views

See similar Maths IB tutors

Related Maths IB answers

All answers ▸

Prove by induction that 7^(8n+3) + 2 is divisible by 5, where n is a natural number.


How does the right angle triangle definition of sine, cosine and tangent relate to their graphs as a function of angle and to Euler's formula?


What is integration by parts, and how is it useful?


Show that the following system of equations has an infinite number of solutions. x+y+2z = -2; 3x-y+14z=6; x+2y=-5


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning