Question

How to solve this integral-> ∫ [0, x] (1)/(1+t^4) dt=

Answer 1

Use the fundamental theorem of calculus, part 1.

Answer 2

I can't grasp this one the answer includes arctan or ln

Answer 3

substitute .... let t^2 = x maybe?

Answer 4

hmm I'll try it

Answer 5

not =x but something more approriate of course

Answer 6

you mean [0, t^2]

Answer 7

\[\int_{0}^{x}\frac{1+t^4-t^4}{1+t^4}dt\]
\[\int_{0}^{x}1-\frac{t^4}{1+t^4}dt\]
if t^2 = a

2t dt = da, t dt = da/2t

\[\int_{0}^{x}1-\frac{t^4}{1+a^2}\frac{da}{2t}\]
\[\int_{0}^{x}1-\frac{t^3}{1+a^2}\frac{da}{2}\]
\[\int_{0}^{x}1-\frac{a\sqrt a}{1+a^2}\frac{da}{2}\]
might be better with a trig sub .... or may just be a pain regardless

Answer 8

http://www.wolframalpha.com/input/?i=integrate+1%2F%281%2Bx%5E4%29

the wolf says its ugly .... so the question is, do we need to integrate it or is this part of taking the derivative of th eintegration?

Answer 9

1-t^4+t^8-t^12 ...
--------------------
1 + t^4 | 1
-(1+t^4)
--------
-t^4

\[\int(1-t^4+t^8-t^{12}+ ...)\]
\[t-\frac 15t^5+\frac19t^9-\frac1{13}t^{13}+ ...\]
at t=0 is 0, so let t=x

Answer 10

Hmmm bit more than I can handle that's for sure

Answer 11

Is there are way I do a reversal trick with the answers given

Answer 12

A way I can do*

Answer 13

im not too sure what you mean by that

Answer 14

Okay so I have the answer chooses is there an inverse I can to on the choices that would will give me the original integral

Answer 15

what are the choices ... that might help me see a solution better

Answer 16

1/2 arctan(x^2) 1/2 arctan(x^4) 1/2 ln(1+x^4) 1/2arcsin(x^2)

Answer 17

well, i know what the derivative will be .....\[\frac{d}{dx}\left(\int_{0}^{x}f(t)~dt\right)=\frac{d}{dx}\left[F(x)-F(0)\right]=f(x)x'-f(0)0'=f(x)x'\]

Answer 18

so, which of these answers has a the derivative of x'/(1+x^4) ?

Answer 19

give me a sec

Answer 20

so the first one is x/x^4 +1

Answer 21

the rest of them don't match

Answer 22

so A is the best bet, unless we can work some algebra on the others perhaps?

Answer 23

No no I can't so I'll choose a

Answer 24

Thanks though

Answer 25

the wolfs answer is ugly, not as pretty as those so its hard to dbl check :)

Answer 26

Yeah I know I tried other calculators

Answer 27

the partial fraction is messy too, which then leads to the messy integral lol