Question

Evaluate the integral question inside!

Answer 1

\[\frac{x^{2} dx }{x^3-e^3}\]

Answer 2

e^3 is a constant

Answer 3

Clue: u is usually thingy on the bottom
u would have a du on top

Answer 4

Here is my answer: \frac{1}{3} ln (x^{3} - e^{3}) + C

Answer 5

u = x^3 - e^3 ; du = 3x^2 dx ; dx = du/3x^2

Answer 6

eek!

Answer 7

x^2 du
-------
3x^2 u



du
----- = (1/3) ln(u) +C
3 u

Answer 8

i wonder: (x^3-e^3) is a difference of cubes; can we split it to simplify further?

Answer 9

(x-e)(x^2 +x e +e^2) :)

Answer 10

yay! that's the answer I have!
\[\frac{1}{3} \ln (x^{3} - e^{3} ) + C\]

Answer 11

leave it :)

Answer 12

hmph! Not the final answer?

Answer 13

lol!

Answer 14

Thank you so much for the confirmation!

Answer 15

should we put the 1/3 as an exponent inside the ln?

Answer 16

i dont see much more we can do to simplify it :)

Answer 17

Me either! Phew, you had me worried! lol