Find the integral of (x^6+4)^2 dx

- megannicole51

Find the integral of (x^6+4)^2 dx

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- anonymous

square it!

- anonymous

\[\int(x^{12}+8x^6+16)dx\]

- megannicole51

so....(x^6+4)(x^6+4)? and use foil to calculate?

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## More answers

- anonymous

square, yeah

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- megannicole51

hahah thats funny!

- megannicole51

so is that the answer? i feel like it can't be that simple!

- anonymous

you made it to calculus right? time to drop "foil" from your vocab
and no, that is not the answer, that is how you are going to find the answer right?

- anonymous

integrate term by term

- dan815

the foil bomb

- anonymous

\[\int x^{12}dx+8\int x^6dx+\int 16dx\]

- megannicole51

yeah im in calc 2 and at university....i like calling it foil.

- anonymous

use the power rule backwards for each
\[\int x^ndx=\frac{x^{n+1}}{n+1}\]

- anonymous

you good from there?

- dan815

do they start integration in calc 2?

- megannicole51

yeah they do

- megannicole51

my professor doesnt speak very good english so I'm trying to learn the material and try to understand what hes saying lol

- megannicole51

and what do u mean the power rule backwards?

- dan815

watch youtube videos on it there are a lot

- dan815

derivative backwards

- dan815

just think what do i need to take the derivative of to get that

- dan815

like 16...
d/dx of 16x = 16

- dan815

d/dx of 16x+c is also=16

- megannicole51

ooooh i get it but how would u do like x^10?

- dan815

for x^6
....
d/dx of 1/7*x^7 = x^6

- megannicole51

so it would be x^9?

- anonymous

\[\int x^{10}dx=\frac{x^{11}}{11}\] etc

- dan815

d/dx 1/11 * x^11=x^10

- anonymous

add one to the exponent, then divide by that number

- dan815

u addin +1 to exponent and dividing by thaat exponent

- dan815

the inverse of derivative power formula

- anonymous

this is what i means by the power rule backwards
\[\int x^ndx=\frac{x^{n+1}}{n+1}\] since the power rule is
\[\frac{d}{dx}[x^n]=nx^{n-1}\]

- dan815

for derivavtive u multiple my exp then subtract -1 from exp
so backwards is
+1 to exp and divide by exp

- dan815

u multiply*

- anonymous

power rule
multiply by the exponent, drop the power by 1
power rule backwards
add one to the exponent, divide by it

- dan815

loser!! buddy

- dan815

hows java coming along

- megannicole51

so if i had the integral of (x^12 dx+8) that would just be x^11?

- dan815

no

- megannicole51

okay im confused im sorry

- dan815

ok ill make it simple

- dan815

derivative of x^2 =?

- megannicole51

2x

- dan815

integral of 2x =?

- megannicole51

2?

- dan815

no its x^2

- megannicole51

okay

- dan815

try this

- megannicole51

okay:)

- dan815

3x^2

- dan815

integral of that?

- dan815

its gonna be confusing for the first week u will mix up derivatives and integrals, we all did, but u will get used to it

- megannicole51

okay i dont understand how you are taking the integral simple equations....i dont remember how to do them

- megannicole51

thanks for the reassurance :)

- dan815

okAY look carefully what we are doing for derivative

- megannicole51

yes i can take the derivative

- dan815

d/dx of x^3 =

- megannicole51

3x^2

- megannicole51

so the integral is x^3?

- anonymous

\[\int xdx=\frac{x^2}{2}\\\int x^2dx=\frac{x^3}{3}\\\int x^3dx=\frac{x^4}{4}\\\int x^4dx=\frac{x^5}{5}\\\int x^ndx=\frac{x^{n+1}}{n+1}\]

- dan815

yeah

- dan815

break up the steps though, so for derivative u first multipled by the exponent and subtracted 1 from the exponent

- megannicole51

so x^12 is x^13/13?

- dan815

yes

- megannicole51

ooooh okay

- megannicole51

so what do u do if u just have say 5?

- dan815

5x

- dan815

theres a catch to all this though, there can be a constant there too

- dan815

for example d/dx 5x+1 = 5
so is d/dx 5X +2 = 5
d/dx 5x+c = 5

- dan815

so just keep doing whatever u are doing, but after u get ur integral answer just add a c to it

- megannicole51

okay so for the actual problem it would be the integral of x^13/13+8x integral x^7/7 dx + integral 16x dx?

- megannicole51

sorry i dont know how to make my equations look fancy lol

- dan815

the integral and dx sighs are lost once u do the integration buy yes

- megannicole51

so is that the answer to the problem? or is there more?

- dan815

x^13/13+8x +x^7/7 +16x +c

- dan815

that sthe answer

- dan815

u can simplify it but ya

- megannicole51

why is it set up like that? do u know?

- dan815

like what

- megannicole51

why do they take out the integrals?

- dan815

its just an operator sign like d/dx

- dan815

after u do d/dx of 5x

- dan815

u will get 5 not d/dx of 5 right

- megannicole51

my online thing says its wrong:(

- dan815

samething with integral and dx
d/dx mEANS DERIVATIVE WITH RESPECT TO X
integral dx means integral with respect to x

- megannicole51

so like change the 8x to 8? and 16x to 16?

- dan815

what do u mean

- megannicole51

the answer was wrong is there something we are missing?

- dan815

did u add the c

- megannicole51

yes

- dan815

try without it then

- megannicole51

nope didnt work

- dan815

what are u entering

- megannicole51

x^13/13+8x+x^7/7+16x+c

- dan815

its 8x^7/7

- dan815

why dont u add the 8x and 16x together too

- megannicole51

then is it 16x^15/15?

- dan815

wuuttt lool

- dan815

where did that come from

- megannicole51

because you took the 8x and made it 8x^7/7
and adding the 8x and 16x didnt work

- dan815

no i made the x^7/7 8x^7/7

- megannicole51

ooooooh lol

- dan815

lol

- megannicole51

nope that didnt work either

- dan815

i remember these noob integration days... it seemed so confusing, i was looking at my teacher like some alien

- megannicole51

exactly! lol i feel so lost and i have so much homework

- dan815

dont woory in a week or 2 it will be 2nd nature

- megannicole51

yeah i hope so....so what did we do wrong with this one:(

- dan815

wait ill brb

- megannicole51

is it in the beginning where we just distributed the 2 instead of using foil to solve the equation?

- dan815

okay let me show you all the steps

- dan815

(x^6+4)^2

- dan815

|dw:1377741247034:dw|

- megannicole51

lol i totally left the 8x in my answer hahaha im sorry i just didnt catch it

- megannicole51

thank you so much for all of ur help.... :) wana help me with another one?:)

- dan815

ok

- dan815

just practice more u need to do lke atleast 50 more integration questions

- dan815

i think ive integrated like 1000000 times since last year

- dan815

definately more integration that derivatives

- megannicole51

hahah yeah i need a lot more practice lol
the integration of sin^3(8q) cos (8q) dq

- dan815

|dw:1377742500209:dw|

- megannicole51

is that 8*4 in the denominator?

- dan815

yes

- megannicole51

okay:) and then do the same for cos(8q)?

- dan815

no ur done

- dan815

u r

- dan815

|dw:1377742649267:dw|

- dan815

take its derivative

- megannicole51

chain rule?

- dan815

|dw:1377742693679:dw|

- megannicole51

okay hold on brb

- megannicole51

so it would be (32)(32sin8q*cos8q)-(sin^4(8q))/32^2

- dan815

|dw:1377744098142:dw|

- dan815

|dw:1377744110551:dw|

- dan815

see it works

- dan815

|dw:1377744217683:dw|

- megannicole51

so is that the answer? why did i do the chain rule?

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