Question

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

Answer 1

square it!

Answer 2

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

Answer 3

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

Answer 4

square, yeah

Answer 5

hahah thats funny!

Answer 6

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

Answer 7

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?

Answer 8

integrate term by term

Answer 9

the foil bomb

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

you good from there?

Answer 14

do they start integration in calc 2?

Answer 15

yeah they do

Answer 16

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

Answer 17

and what do u mean the power rule backwards?

Answer 18

watch youtube videos on it there are a lot

Answer 19

derivative backwards

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

so it would be x^9?

Answer 26

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

Answer 27

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

Answer 28

add one to the exponent, then divide by that number

Answer 29

u addin +1 to exponent and dividing by thaat exponent

Answer 30

the inverse of derivative power formula

Answer 31

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

Answer 32

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

Answer 33

u multiply*

Answer 34

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

Answer 35

loser!! buddy

Answer 36

hows java coming along

Answer 37

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

Answer 38

no

Answer 39

okay im confused im sorry

Answer 40

ok ill make it simple

Answer 41

derivative of x^2 =?

Answer 42

2x

Answer 43

integral of 2x =?

Answer 44

2?

Answer 45

no its x^2

Answer 46

okay

Answer 47

try this

Answer 48

okay:)

Answer 49

3x^2

Answer 50

integral of that?

Answer 51

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

Answer 52

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

Answer 53

thanks for the reassurance :)

Answer 54

okAY look carefully what we are doing for derivative

Answer 55

yes i can take the derivative

Answer 56

d/dx of x^3 =

Answer 57

3x^2

Answer 58

so the integral is x^3?

Answer 59

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

Answer 60

yeah

Answer 61

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

Answer 62

so x^12 is x^13/13?

Answer 63

yes

Answer 64

ooooh okay

Answer 65

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

Answer 66

5x

Answer 67

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

Answer 68

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

Answer 69

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

Answer 70

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

Answer 71

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

Answer 72

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

Answer 73

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

Answer 74

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

Answer 75

that sthe answer

Answer 76

u can simplify it but ya

Answer 77

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

Answer 78

like what

Answer 79

why do they take out the integrals?

Answer 80

its just an operator sign like d/dx

Answer 81

after u do d/dx of 5x

Answer 82

u will get 5 not d/dx of 5 right

Answer 83

my online thing says its wrong:(

Answer 84

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

Answer 85

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

Answer 86

what do u mean

Answer 87

the answer was wrong is there something we are missing?

Answer 88

did u add the c

Answer 89

yes

Answer 90

try without it then

Answer 91

nope didnt work

Answer 92

what are u entering

Answer 93

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

Answer 94

its 8x^7/7

Answer 95

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

Answer 96

then is it 16x^15/15?

Answer 97

wuuttt lool