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/sci/ - Science & Math

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3117220 No.3117220 [Reply] [Original]

Hi guys.
I've been having problems with a calculus example exercise. In the image, as you can see, the exercise is solved in three steps after the "Original" exercise: "Rewriting", "Integrate" and "Simplifying".
The thing is I have no idea what did they do to the "Original" to obtain the "Rewriting" step:
they turned this "cbrt(x)(x - 4)" where cbrt is cubic root,
into this "x^(4/3) - 4 x^(1/3)".
If the exercise where to begin in the "Rewriting" step i would't have any problems whatsoever.
So i'm not asking you to help me solve the entire exercise, I only want you explain me what happened between "Original" and "Rewriting".
I don't care if you call me stupid for this, but i would really appreciate it if you can help me with this one.
Forgive me if i sound rude or just stupid. English is not my main language.
Thanks beforehand guys.

>> No.3117225

Distribute

<span class="math"> x^{1/3}[/spoiler]

<span class="math"> x^{1/3} \cdot x = x^{\frac{4}{3}}[/spoiler]
through

>> No.3117228

(x^1/3)((x^1)-4^1) = x^1+1/3-4^1+1/3

There you go.

>> No.3117231

The cube root of X is equivalent to X to the 1/3.

<div class="math">\sqrt[3]{x} = x^{1/3}</div>

>> No.3117235

"I get the messy integration and simplifying, but I just don't know anything about basic laws of exponents!"

Fuck you, troll.

>> No.3117246
File: 369 KB, 450x457, tumblr_l59a4gda8J1qa14pno1_500.gif [View same] [iqdb] [saucenao] [google]
3117246

>>3117225
Thanks man.
Now i feel like an idiot.
That happens when an i'm-bad-at-algebra stupid guy like me tries calculus.
I need to buy a good algebra and trigonometric book-
I swear to god i'll get good at this.
Also, that's the downside of self teaching math T-T. I often get beaten by a single exercise.

Well, thanks anyway Anonymous. I love you whoever you are.

>> No.3117247

>>3117231
<div class="math">\sqrt[3]{x} = x^{1 \over 3}</div>
practicin' mah tex

>> No.3117250

Thanks to you all anonymous. I don't know if you are the same or different people, but i love you alls, and i knew i could count on you

>> No.3117261

>>3117246
The trick about math (especially as you get into calculus and beyond) is that, like natural language, the unwritten rules are just as important as the written ones. People just get a "knack" and learn to follow the rules without being able to tell you what they are.

You need to solve a LOT of problems to develop a knack for solving problems. Generally, far more than you get in any given textbook.