Question

Evaluate the integral:
int/ 7u^2-(2/u)

Answer 1

\[\int 7u^2 - \frac 2u?\]

Answer 2

yes

Answer 3

split the integral..

\[\int 7u^2 du - \int \frac{2}{u} du\]
do you know how to integrate those?

Answer 4

no i do not

Answer 5

what if i take out the constants..
\[7\int u^2 du - 2\int \frac 1u du\]

Answer 6

do those ring a bell?

Answer 7

5(1/u)^2?

Answer 8

\[\int x^ndx={x^{n+1}\over n+1}+C\]and\[\int\frac1xdx=\ln|x|+C\]

Answer 9

where are the n's coming from

Answer 10

these are definitions and rules

Answer 11

n is just a variable

Answer 12

so it would be 7^(u+1)/u+1 and ln lul

Answer 13

hmm nope..the base is supposed to be u

Answer 14

\[\int u^3 du = \frac{u^{3+1}}{3+1}\]
\[\int u^4 du = \frac{u^{4+1}}{4+1}\]
getting the thread?

Answer 15

yes

Answer 16

so what's u^2

Answer 17

so is it 7(u^3/2+1)?

Answer 18

9? or 4?

Answer 19

what do you mean 9 or 4?

Answer 20

okay i guess i dont know what u^2 is

Answer 21

you were close! simplify \[7(\frac{u^3}{2+1})\]

Answer 22

7u^3/21?

Answer 23

what's 2+1?

Answer 24

3

Answer 25

int udv=uv - int v du

Answer 26

then it\s\[\frac{7u^3}{3}\]
got it/

Answer 27

yes i just shouldnt have multiplied the 2+1 times 7

Answer 28

its saying that that isnt the correct answer though

Answer 29

lol there's still \(2\int \frac 1udu\) remember

Answer 30

arg.. i hate this

Answer 31

lol look at what turing said
\[\int \frac 1x dx = \ln x\]
so what's \[\int \frac 1u du/\]

Answer 32

ln u

Answer 33

but i dont know where to put that now..

Answer 34

so combine...

Answer 35

\[\int 7u^2du = \frac{7u^3}{3}\]
\[2\int \frac 1u du = 2\ln u\]
so what's \[\int u^2 du - 2\int \frac 1u du?\]

Answer 36

there's a 7 on the first term

Answer 37

5(1/u)?

Answer 38

or just 5? im not sure

Answer 39

what? what did you do?

Answer 40

i dont know im guessing because i dont know what to do

Answer 41

14(1/u)?

Answer 42

analyze my last post carefully

Answer 43

you\'re just going to substitute

Answer 44

7(1/u)^2?

Answer 45

the question is \[\int 7u^2 du - \int \frac{2}{u} du\]
correct?

Answer 46

yes. i just havent learned about subtracting them before

Answer 47

what's \[\int 7u^2 du?\]

Answer 48

21u^3?

Answer 49

how?

Answer 50

i dont know im basically guessing because i do not know what to do!

Answer 51

14u^3?

Answer 52

7*(2/u)^2??

Answer 53

but i already told you how to do it..why guess

Answer 54

scroll up

Answer 55

becuase im not understanding how your telling me to do it! it isnt making any sense to me!

Answer 56

im really not good at this!

Answer 57

do you agree that \[\int u^2du\] is in the form \[\int x^n dx?\]

Answer 58

yes

Answer 59

\[\int x^n dx = \frac{x^{n+1}}{n+1}\]

Answer 60

this is a rule

Answer 61

this is called the power rule

Answer 62

alright so what does that do for my problem

Answer 63

in \[\int u^2 du \]
which is the counterpart of x?

Answer 64

u?

Answer 65

correct and hwhat is the counterpart of n

Answer 66

2

Answer 67

side note (sorry to interrupt) @drumjockey83 memorize the part that says "common integrals"
http://tutorial.math.lamar.edu/pdf/Calculus_Cheat_Sheet_All.pdf

it will make your life so much easier

Answer 68

thank you

Answer 69

so how what will be \[\frac{x^{n+1}}{n+1}\] here?

Answer 70

u^(2+1)/2+1?

Answer 71

so what will be*

Answer 72

correct

Answer 73

so \[\int u^2 du \implies \frac{u^{2+1}}{2+1} \implies \frac{u^3}{3}\]
do you get that?

Answer 74

yes

Answer 75

so wjat os \[7\int u^2 du?\]

Answer 76

7u^(2+1)/2+1?

Answer 77

correct. but simplify

Answer 78

7(u^3/3)?

Answer 79

nnice

Answer 80

thats the answer?

Answer 81

nope..that's just for \[\int 7u^2 du\]

Answer 82

okay i thought we already went over that

Answer 83

now we solve \[2 \int \frac 1u du\]
well im trying to go from the beginning because you're geting confused somewhere..idk which

Answer 84

what would be the answer to that one

Answer 85

2(1/u)?

Answer 86

nope. here's a hint.another integration rule
\[\int \frac 1x dx = \ln x\]
so what's \[\int \frac 1u du?\]

Answer 87

ln u

Answer 88

so what's \[2\int \frac 1u du\]

Answer 89

im not sure!! i dont know whay to do with that 2!!

Answer 90

2 ln u???

Answer 91

correct

Answer 92

so whats the complete answer
?

Answer 93

so what's \[\int 7u^2 du - \int \frac 2u du?\]

Answer 94

7(u^3/3)-2 ln u

Answer 95

correct

Answer 96

congrats ^_^

Answer 97

its saying that that isnt right

Answer 98

do you have choices?