find the antiderivative of x^2/((2x^3-12)^4) using substitution

Question

tinyclown · Answer

now what i got was -1/(24(2x^3-12)^3)) + C

tinyclown · Answer

and to check, i did the antiderivative on wolfgram and got -1/(144(x^3-6)^3)) or something i don t remember

tinyclown · Answer

i graphed both of those and they were the same function but

tinyclown · Answer

neither is an answer to the quiz question (it s multiple choice)...now there is an option that says none of the above but also says that the problem can t be solved through substitution despite the fact that s exactly how i solved it

zepdrix · Answer

Hmm maybe your coefficient is a little off..
I'm coming up with -1/18 as opposed to your -1/24

tinyclown · Answer

okay so that s actually one of the options let me recheck my math

zepdrix · Answer

$$\large\rm \int\limits\frac{x^2dx}{(\color{orangered}{2x^3-12})^4}$$
$$\large\rm \color{orangered}{u=2x^3-12},\qquad\qquad du=6x^2dx,\qquad\qquad\frac{1}{6}du=x^2dx$$

zepdrix · Answer

Yah maybe something got mixed up with your power rule :)
You should get a -1/3 when integrating,
not a -1/4.

tinyclown · Answer

oh yeah yeah that s right !! thank you so much !!

zepdrix · Answer

np