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Did you find the derivative to check yourself?

To keep things simple, you may try u-substitution
\(u = 6-x\)

no i didn't find the derivative to check my answer, i would find the derivative of my problem right?

he might heard of it
I don't know

Im not sure i have, but i took the derivative and got x^2-12x+36x :)

x^3-12x^2+36x?

yeah its just that i had x(x^2-12x+36)

got it right! thanks!!

how do you know ` x(x^2-12x+36) ` is same as the original function ?

that might be a dumb q hmm

x(6-x)^2
think he expanded the square thingy first

she* and yeah i did

Ahh looks great she :D

oops sorry

do you want to see the sub thingy mentioned by ganeshie8 for fun?

Its okay! sure is it easier than finding the derivative?

Oh okay, I didnt understand the substitution part at first, but i get it now! thanks for explaining!

oops I didn't multiply correclty

my answer is off
because when I did -6(u^2) I put -6u
and so I integrated the wrong thingy

but that is sorta how works above if you can multiply correctly :p

try this if you're loving antiderivatives :
\[\int x(6-x)^{9999999}\,dx = ?\]

im not sure i did it right though

differentiate your answer and see if you get back the original function

also what happened to the constant, C

nvm I just did it again and got 4x^3/2/3 +6 -sinx +C

you're doing calculus, that means you're not in highschool anymore
time to use proper notation

4x^ `3/2/3` +6 -sinx +C
what does that even mean

[(4x^3/2)/3] +6-sinx+C
Btw you can take calculus in high school, just saying

Much better, but still it is not mathematically correct

pretty sure you meant
[(4x^3/2)/3] +6(-sinx)+C

why is it +6(sin(x)) and not -sin(x)?

yes!

forgot to put + some constant at the end there

oh so you got derivative and antiderivative mixed up

but just so you know if it was taking derivative of 6cos(x)
you would put -6sin(x) and not 6-sin(x)

but yeah antiderivative of 6cos(x) would be 6sin(x)
since the derivative of 6sin(x) is 6cos(x)

the antiderivative of 6cos(x) would be 6sin(x)+C
since the derivative of 6sin(x)+C is 6cos(x)
*

the most general antiderivative *

Okay I understand now! thanks a lot!!

np