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# How to integrate 3(root)x Watch

1. Integrate the cube root of x (edited)

I think it's the same as x^(3/2) and then you add one to the power making it 5/2 so it becomes x^(5/2)/5/2?

The markscheme says its , how?
2. (Original post by Magenta96)
Integrate 3(root)x.

I think it's the same as x^(3/2) and then you add one to the power making it 5/2 so it becomes x^(5/2)/5/2?

The markscheme says its , how?
Are you integrating or, as the answer suggests
3. i think you mean "integrate the cube root of x"...

well this is x1/3 so add 1 to the power and divide by the new power... and add c
4. (Original post by the bear)
i think you mean "integrate the cube root of x"...

well this is x1/3 so add 1 to the power and divide by the new power... and add c
oh right yeah it so I get up to this part:
divided by 4/3, how do they manage to get 3/4 as the co-efficient?
5. Reverse power rule!

They get 3/4 as the coefficient as it's been switched around from division to multiplication.
6. (Original post by Frankster)

Therefore, add one to the power: 3/2. And also divide 3 by 3/2 = 2

so u get
I've edited the q, it's actually asking to integrate the cube root of x
7. (Original post by Magenta96)
oh right yeah it so I get up to this part:
divided by 4/3, how do they manage to get 3/4 as the co-efficient?
if you divide by a fraction you multiply by its reciprocal
8. (Original post by the bear)
if you divide by a fraction you multiply by its reciprocal
ohhh right, thanks I forgot all about that
9. Ok, so to integrate, you add one to the power and divide by the new power.

$\sqrt[3]{x} = x^{\frac{1}{3}}$

$\frac{1}{3}+1 = \frac{4}{}3$

$\frac{x^\frac{4}{3}}{\frac{4}{3}} = \frac{3}{4}x^{\frac{4}{3}}$

Because

$\frac{1}{\frac{4}{3}} = \frac{3}{4}$

Get it?
10. (Original post by Banny Dyrne)
Ok, so to integrate, you add one to the power and divide by the new power.

$\sqrt[3]{x} = x^{\frac{1}{3}}$

$\frac{1}{3}+1 = \frac{4}{}3$

$\frac{x^\frac{4}{3}}{\frac{4}{3}} = \frac{3}{4}x^{\frac{4}{3}}$

Because

$\frac{1}{\frac{4}{3}} = \frac{3}{4}$

Get it?
yes, thank you

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Updated: April 9, 2013
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