Fundamental Theorem of Calc Problem using Chain Rule

[ManicPIxie]

Homework Statement

F(x) = (integral from 1 to x^3) (t^2 - 10)/(t + 1) dt
Evaluate F'(x)

Homework Equations

Using the chain rule

The Attempt at a Solution

Let u = x^3
Then:
[((x^3)^2 - 10) / (x^3 + 1)] ⋅ 3x^2
*step cancelling powers of x from fraction*
= (x^3 - 10)(3x^2)
= 3x^5 - 30x^2

I am trying to input a solution to a Maple TA problem for uni work, is this answer incorrect, or is possible that my maple TA syntax is incorrect.
My attempted answer on maple looked like:
(3*x^5) - (30*x^2)

Any help that *doesn't* just give me the answer is very much appreciated!

 

[ShayanJ]

[((x^3)^2 - 10) / (x^3 + 1)] ⋅ 3x^2

This is correct. But what happened to the denominator after this?

 

[ManicPIxie]

This is correct. But what happened to the denominator after this?

In the cancelling step:
[(3x^6 - 10)/(x^3 + 1)] ⋅ 3x^2
It canceled to give:
(x^3 - 10) ⋅ 3x^2

 

[ShayanJ]

In the cancelling step:
[(3x^6 - 10)/(x^3 + 1)] ⋅ 3x^2
It canceled to give:
(x^3 - 10) ⋅ 3x^2

You can't do that!
I don't even see how you're making that mistake to explain why its wrong!

 

[ManicPIxie]

You can't do that!
I don't even see how you're making that mistake to explain why its wrong!

:/ Okay, my bad.

Retry:
[(x^6 - 10)/(x^3 + 1)] ⋅ 3x^2
= (3x^8 - 30x^2)/(x^3 + 1)

 

[ManicPIxie]

Aha! And entering that into Maple TA works!
Thanks for your help!