Question

Fastest way to integrate:

dx/ (1 + x^4 )

Answer 1

kidding..

Answer 2

this is the same as dx / ( 1 + (x^2)^2 )

Answer 3

let u = x^2 , du = 2x dx ,

Answer 4

I don't think that substitution would help.

Answer 5

its a start

Answer 6

x^2=tan x
naw...

Answer 7

du/(2x) = dx

Answer 8

and what do you propose to do with that x ?

Answer 9

we can solve for x, we know that u = x^2, so x = sqrt u

Answer 10

so I get integral 1 / [ u^1/2 * (1 + u^2) ] du

Answer 11

thats a known integral

Answer 12

you have to check your table of integrals

Answer 13

I don't like tables, this should be derivable...

Answer 14

Agreed.

Answer 15

dont forget the 1/2
integral 1/(1+x^4) = 1/2 integral 1 / [ u^1/2 * (1 + u^2) ] du

Answer 16

What if I add subtract x^2 , then seperate it.
Okay this may work.

Answer 17

no i dont think that would work

Answer 18

looks very complicated
http://www.wolframalpha.com/input/?i=int%28dx%2F+%281+%2B+x^4+%29+%29

Answer 19

\[I = 1/2 \int\limits ( 1+ x^2)/(1+x^4) + (1-x^2)/(1+x^4)\]

Answer 20

maybe complete the square?

Answer 21

Now we just multiply divide by x^2

Answer 22

you added and subtracted x^2 on top?

Answer 23

I didn't think wolfram would be promising...
completing the square would give\[\int\frac{dx}{(x^2-1)^2+2x^2}\]which would not help I don't think

Answer 24

here http://answers.yahoo.com/question/index?qid=20080721154424AAYOrmH

Answer 25

there doesnt look like theres a fast way

Answer 26

Oh dear.

Answer 27

so the trick is
add and subtract 2x^2 on the bottom, which forces a perfect square

Answer 28

i wouldnt have thought of this , :0

Answer 29

well, it turns out completing the square can pay off...
might as well do this with PF if it's gonna be that big of a hassle

Answer 30

then you can use partial fractions

Answer 31

, can you generally complete the square on any function, only for quadratics, and perhaps even functions . here we got lucky

Answer 32

I did that above, but I didn't see where to go from there :/

Answer 33

, in fact, this can lead to a general integral formula for dx / ( 1 + x^(2n) )

Answer 34

, for n > 1

Answer 35

ok you want to do it step by step
ill make a trade with you, you help me with my simple 'work' problem. its just an integral

Answer 36

the units stump me , im not so confident about it

Answer 37

oh cool, wikipedia already has the formula
http://en.wikipedia.org/wiki/List_of_integrals_of_rational_functions

Answer 38

scroll down to dx/ ( 1 + x^(2n) )

Answer 39

so you want to go through the steps on yahoo?

Answer 40

Okay.
I think this works too. Similar though.

\[(1-x^2)/(1+x^4) = (1/x^2 -1)/(x^2 + 1/x^2) \]

Now use \[x - 1/x = t => dt = numerator\]
\[t^2 = 1/x^2 + x^2 -2 => t^2 + 2 = denominator\]

Answer 41

i know whats going on, the homework was dx/ (x^4 - 1) , and you made a typo. no teacher would give this assignment for baby math people

Answer 42

That helps Right?

Answer 43

maybe, did you do it out ?

Answer 44

or the teacher made a typo, this assignment is probably too difficult for calculus students

Answer 45

Yep.
Look the integral now becomes:
\[dt/( 1+t^2)\]

Answer 46

No. No mistake.
This does work.
Wait I'll write all the steps.

Answer 47

oh ok

Answer 48

you should get the answer
[1/(2√2)] arctan (√2x +1) + [1/(2√2)] arctan (√2x - 1) + c

Answer 49

so what did you do ?

Answer 50

I didnt write the final few steps.
But its easy after that.

Answer 51

theres a mistake
your first line is wrong

Answer 52

Luella has a pond in her yard. She wants to surround it with 330 feet of fencing. The fencing is sold by the yard. How many yards should she buy?

Answer 53

someone check my answers
http://prntscr.com/mls3hl

Answer 54

https://i.imgur.com/Wjmpc6D.png

Answer 55

Assessment items
Assessment started: undefined.
Item 1

Read the passage.

Dark Star

Giselle leaned against the mahogany bay horse, stroking the white diam

Answer 56

Okay I was gone for a minute BUT I'M BACK NOW

Answer 57

the scatter plot presents Ray's monthly electricity bills and amount of time ray

Answer 58

Which word shares a connotative meaning with the word cheap as it is used in this sentence?

Ashley thought her parents were being cheap when they bought ge

Answer 59

Which revision fixes the dangling modifier in the sentence?

Rowing through the rapids, the canoe began to fill with water.

Answer 60

dangling modifier

Answer 61

Misplaced Modifiers

Answer 62

For which literary work did Joseph Heller use his military experiences as a prima

Answer 63

Calc III Tutorial: Lagrange Multipliers

Answer 64

Can someone translate this for me?

Answer 65

Find the interest due on $1,090 at 8% for 5 years.

43.60
68.13
436.00
681.25

Answer 66

Now identify the simple subject and simple predicate.

The meeting began promptly at seven o'clock.

Answer 67

What can be inferred from these lines describing the pardoner in Chaucer's prolog

Answer 68

What is the rate of change of the linear relationship modeled in the table?

x y

Answer 69

Which of these best identifies the shift of mood in this sentence?

"If you were to sit more comfortably, you will not fall off.

Answer 70

Which scenario best matches the linear relationship expressed in the equation y = u221214x + 1,700?

Kent has $1,700 in his bank account and spends $14 each

Answer 71

The saying "Whoso is a man must be a nonconformist" is based on whose transcendentalist belief?
A.