Integrate (x^2 +2)(2x-6) with respect to x.

For a simple integration like this, begin by expanding the brackets to get 2x3-6x2+4x-12. Next each term should be integrated with respect to x, begin with the first term, each peer should be raised by 1, and then the whole term should be divided by the new power. eg. 2x3 ->2x4 and is then divided by its new power, to become 2x4/4 which simplifies to x4/2. This is continued for each term. Remember that -12 can be though of as -12x0 and therefore this will become -12x. Finally a constant must be added to the end of the solution as it is unknown what term could be lost when differentiating, it is common practice to use +C or +k. When all the terms are found, they are added together to get the solution which is, x4/2 -2x3+ 2x2-12x + C.

NB
Answered by Nicholas B. Maths tutor

3049 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A particle P is projected vertically upwards from a point 20m above the ground with velocity 18m/s, no external forces act on it other than gravity. What will its speed be right before it hits the ground? Give your answer to one decimal place.


Find the equation of the tangent to the curve y = 4x^2 (x+3)^5 at the point (-1, 128).


How do one tailed and two tailed hypothesis tests differ


A particle P moves with acceleration (-3i + 12j) m/s^2. Initially the velocity of P is 4i m/s. (a) Find the velocity of P at time t seconds. (b) Find the speed of P when t = 0.5


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