Question

find the antiderivative of (2x+6)^3

Answer 1

we havent learned how to find antiderivatives of a function raised to a power so im not quite sure where to start

Answer 2

Yes you have. What's the derivative of x^4?

Answer 3

4x^3

Answer 4

So, what is the antiderivative of 4x^3?

Answer 5

x^4

Answer 6

Okay, how about the antiderivative of (x+2)^3?

Answer 7

would it be (x+2)^4?

Answer 8

Very Close! \[\frac{d}{dx}(x+2)^{4} = 4(x+2)^{3}\] See that factor of 4 out in front? This makes the requested antiderivative ¼(x+2)^4. Find the derivative of that and convince yourself.

Answer 9

ooooo i seeee
so the antiderivative of (2x+6)^3 is (1/4)(2x+6)^4