Question

Evaluate the integral of x^2(x^3+1)^3

Answer 1

You can use U, du substitution where u=x^3+1. Do you know how to do this?

Answer 2

Not really, I didn't understand it when it was explained to me

Answer 3

when u=x^3+1
to find du, you take the derivative of u

Answer 4

What do you get as du?

Answer 5

3x^2

Answer 6

du=3x^2dx
In order to substitute dx you replace everything you can with du.
Since we only have a x^2dx, we have to get rid of the 3.
You can get 1/3du= x^2dx.
Just replace x^2dx with the 1/3 du, and replace x^3+1 with u

Answer 7

what do you get?

Answer 8

I'm confused as to where I should be plugging that in, I'm sorry

Answer 9

well where you see the x^3+1, take that out and put a u

Answer 10

from the original integral i typed out?

Answer 11

Yes.

Answer 12

But you said u= x^3 +1

Answer 13

yes, since x^3+1 is the same thing as u, you can just substitute it.

Answer 14

integral of x^2 u dx

Answer 15

*u^3

Answer 16

Yes, but then subsititute the x^2 dx with 1/3du

Answer 17

okay, so integral of u^3 * 1/3 du

Answer 18

is that right?

Answer 19

Yes. Now take the integral of that.

Answer 20

I realized what I've been doing wrong

Answer 21

would you be willing to check the answer for me?

Answer 22

Yes. But what did you get at the integral of that in terms of u

Answer 23

(u^4)/12 +c, then you just go back and plug in the value for you and you get the answer of (x^3+1)^4/12 + c

Answer 24

thank you so much!

Answer 25

No problem! I am glad I could help!