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I have never seen a indefinite integral represented like this.

This can't be right, |x| stays positive but the x^3 can get negative.

I am not sure though. and I can be wrong.

For negative x, x^3 * |x| = (-x)^3 (-(-x)) = -x^4

What's wrong piece wise representation?

wait... my piece wise is gonna give same result as yours

so, either we are both wrong or right

\[\huge \int\limits\limits_{}^{}|x|^3 dx = {sgn(x)}* \frac{x^4}{4}+c\]

and your integral does seems better

ohh yeah

sgn(x) how could i not think about it!?!?! :(

so, there are multiple ways of representing same integral?

because every integral on this page is gonna get you the same result

so, how do you rule out others? and make one right.

-x^4/4 is what we will get.
sgn(-x)x^4/4 = -1* x^4/4

Yes and why is it negative??

I have confused myself lolol

i am confused myself and blabbering :/

Same here LOL. However I wolframed it and it is giving my equation. The sgn(x) one. Ditto . ??

Ok I got it. Taking example always helps

In that case how is my first equation wrong , the very first one I mentioned ??

Your first integral was right as well

My piece wise representation is pelletty :/

Haha. Maths always confuses us even when we have the right answers . :P

yeah hahaha
i never had to integrate such indefinite integrals before.

Why isn't FoolForMath replying?

Only 2 people know the answer to your question @Ishaan94 , @FoolForMath and god himself :P

lol

Lol, I had the answer but I only figured it out why is it working. Thanks to M.se again ;)

0 fans lol

I beat God! by 455 fans

LOLOL

So, the answer is \[ \frac 1 4 |x|^3 \cdot x +C \]

Does it matter, @FoolForMath the position of modulus on either x^3 or x :P