Find the integral of 3x^2 + 4x + 9 with respect to x.

We must first remember that to integrate, we must increase the power by 1 and divide by this new power.

Therefore, to integrate 3x^2 + 4x + 9, we take the first term, 3x^2. Using the above method, we find that the integral of this is (3x^3)/3 = x^3.

Taking the second term, 4x, we find the integral to be (4x^2)/2 = 2x^3.

Taking the final term, 9, we find the integral to be (9x)/1 = 9x.

As the question gives an indefinite integral (an integral without any limits) we must also remember to add a constant, which we can call C.

Therefore, the integral of 3x^2 + 4x + 9 with respect to x is 2x^2 + x^3 + 9x + C.

DJ
Answered by Dylan J. Maths tutor

9306 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The curve C has the equation y = 2e^x -6lnx and passes through the point P with x - coordinate 1. a) Find the equation to the tangent to C at P


Integrate (lnx)/x^2 dx between limits 1 and 5


A curve has parametric equations x=t(t-1), y=4t/(1-t). The point S on the curve has parameter t=-1. Show that the tangent to the curve at S has equation x+3y+4=0.


A curve passes through the point (4, 8) and satisfies the differential equation dy/dx = 1/ (2x + rootx) , Use a step-by-step method with a step length of 0.3 to estimate the value of y at x = 4.6 . Give your answer to four decimal places.


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