Question

Ok more integrals...

see in the comment box ! :)

Answer 1

\[\int\limits 3x ^{2} \sqrt[4]{10+2x^3} (dx)\]

Answer 2

u sub
u=10+2x^2

Answer 3

Is there any relationship between anything here that you notice? Any ideas? Give it your best shot and we'll help you understand.

Answer 4

i know the 3x^2 does this...

\[3x ^{2} \int\limits \]

Answer 5

srry gave it away

Answer 6

Or solomon will give you the answer to this easy problem

Answer 7

I am not going to give the answer, although I can certainly attempt to help. I just started these in class, they are not hard.

Answer 8

The u substituon method I am still grasping...
how can one tell what is U in each equation given ?

Answer 9

i wish i saw this problem as easy, maybe after U-substitution practice I can be a pro !

Answer 10

I got du/dx = 6x^2 (aka u')

Answer 11

well, without giving anything a reason, but just to remember.
When you have an integral of F(x) and this function is contains f(x) and g(x)
u = f(x)
du = derivative of the f(x) that you are subbing for u, times dx
(as if you took the derivative with du/dx and multiplied times the deferential dx on both sides)

Answer 12

yes

Answer 13

du/dx=6x^2
du=6x^2dx

since you only have 3x^2 dx,

then your sub will be
1/2 du=3x^2dx

Answer 14

this is the part I get confused on... :/

"(as if you took the derivative with du/dx and multiplied times the deferential dx on both sides)"

Answer 15

du/dx=6x^2
du=6x^2dx

since you only have 3x^2 dx,

then your sub will be
1/2 du=3x^2dx

Answer 16

I disconnected, sorry./

Answer 17

so after I find the derivative of U i just multiply it by dx ?

Answer 18

\[\LARGE \int\limits_{ }^{ }~\color{red}{3x^2}\sqrt[4]{\color{blue}{ 10+2x^3 }}\color{red}{dx}\]

Answer 19

the red part is 1/2du
and the blue is u

Answer 20

and yes, about what you said.

Answer 21

how did you get 1/2 du

Answer 22

I have
du = 6x^2 dx, right?

Answer 23

yes yes

Answer 24

I only have 3x^2 inside the integral,
so, to get 3x^2 dx, I divide by 2 on both sides

Answer 25

from du = 6x^2 dx
we obtain,
1/2 du = 3x^2 dx

Answer 26

okay so that means we want to split up du/dx ?

Answer 27

\[\LARGE \int\limits_{ }^{ }~\color{red}{3x^2}\sqrt[4]{\color{blue}{ 10+2x^3 }}\color{red}{dx} \]\[\color{red}{\frac{1}{2}}\LARGE \int\limits_{ }^{ }~\sqrt[4]{\color{blue}{ u }}~~\color{red}{du} \]

Answer 28

we split up du/dx by mutliplying times the defferential dx on both sides, then we found 1/that we didn't have the entire du, as we said,

du = 6x^2 dx
and only had 3x^2 dx
and then divided by 2 on both sides.

See how I substituted in colors?

Answer 29

And you know how to integrate forth root of u, and then sub.... I'll be there if you need any help.

Answer 30

ok let me give it a shot and I'll tag you in the comment box ! and thank you

Answer 31

anytime :)

Answer 32

you probably know this,
\[\LARGE \sqrt[4]{u}=u^{1/4}\]

Answer 33

i did but I got stuck for some reason :/

Answer 34

for what reason?

Answer 35

i thought it may have had a special rule :(

Answer 36

you can post everything here, I don't mind if you draw it by hand, as long as I can read it:)

Answer 37

what is the problem?

Answer 38

no, just the power rule.

Answer 39

i am not good with radicals ?

Answer 40

yes you are.

Answer 41

ok ok power rule yes yes i can take it from there

Answer 42

i know! 5/4

Answer 43

alrighty, I am going to get some snacks, and be back. you should be done by then.

Answer 44

\[\frac{ u ^{5/4} }{ 5/4 }\]

Answer 45

can i simplify afterwards or no? normally i leave it as is.

Answer 46

if I would simplify it would be 4/5 u^5/4 ?

Answer 47

you are forgetting something tho.
\[\LARGE{\frac{1}{2}\int\limits_{ }^{ }u^{1/4}~du}\]

Answer 48

oh!! the 1/2

Answer 49

the integral of u, is what you said, but you got to multiply times a half.

Answer 50

yes the 1/2

Answer 51

i need to multiply that in right ? the 1/2

Answer 52

so after i integrate u
can i multiply the 1/2 to it ?

Answer 53

when you got 4/5 u ^5/4
them=n multiply times 1/2

Answer 54

1/2 ( 4/5 u ^5/4) =
2/5 u ^5/4

Answer 55

then we had that u=10+2x^3
so substitute back for u.

Answer 56

I get 2/5 u^5/4

Answer 57

yes

Answer 58

okay so 2/5u^5/4 = 10 +2x^3 ?

Answer 59

not exactly,
2/5u^5/4

substitute back, as we did before, u= 10+2x^3
2/5 (10+2x^3)^5/4

Answer 60

\[\frac{2}{5}(10+2x^3)^{~5/4}\]

Answer 61

which is simplified to,
\[\LARGE \frac{2}{5}(10+2x^3)\sqrt[4]{10+2x^3}\]

Answer 62

okay

Answer 63

so 2/5 u^5/4 is u right?

Answer 64

yes in terms of u, but that is not yet the answer

Answer 65

in u substition we find u first
because we need to plug it in the end ?

Answer 66

we already established that u=10+2x^3
and this is how we integrated,

and now we are substituting back for u

Answer 67

\[\LARGE \frac{2}{5}u^{5/4}\] becomes, \[\LARGE \frac{2}{5}(10+2x^3)^{5/4}\]

Answer 68

OMG

Answer 69

WHAt ?

Answer 70

I just got it ! its similar to algebra ! i was looking at it wrong because if

u= 10 +2x^3
and if I'm substituting 2/5 u^5/4

then all i have to do is plug in what i have which is u! (u= 10 + 2x^3)

right ??

Answer 71

yes, all you are doing after you integrated with u, is just to pug it back in :)

Answer 72

to *plug it back

Answer 73

You are correct.

Answer 74

thank you so much! I think I do have a brain now :)

Answer 75

Just the fact that you think proves that you have a brain. I stole from
"I think therefore I am"

Answer 76

forgot who said the quote.

Answer 77

haha good one ! thank you

Answer 78

Descartes

Answer 79

you welcome...

Answer 80

yes descartes...