Question

Hi, I'm having a bit of trouble finding the integral for 1/(1+x^7) and e^(-x^2) could someone point me in the right direction please?

Answer 1

try wolframalpha.com it shows steps too

Answer 2

not for these two, the steps are unavailable. If you can see the procedures to take let me know

Answer 3

e^(-x^2) isnt this the same as e^(-2x) ?

Answer 4

it aint :)

Answer 5

I don't think so,

Answer 6

there are plenty of functions that are simply not integrateable

Answer 7

true, so do you see any integration technique available to a Calculus 2 student that would solve these 2 equations?

Answer 8

i got books in the library here with tables of integration ... much more extensive than the leaflets in the textbook

Answer 9

would it not be ln[1+x^7]+C?

Answer 10

take the derivative to test it out :)

Answer 11

there is a 7x^6 missing for that to be good; maybe try int by parts?

Answer 12

or fancy substitutions ;)

Answer 13

hmm, ok, ill see about those

Answer 14

suppose we make:

x = z^(1/7)

Answer 15

dx = (z^6)/7 dz

\[\int\frac{1}{1+(x)^7}dx\]
\[\int\frac{z^6}{7(1+(z^{1/7})^7)}dz\]

Answer 16

i messed up the derivative of z^(1/7) i think :)

Answer 17

-6/7

Answer 18

im gonna switch to another variable that stands out better
\[[a^{1/7}]'=\frac{1}{7a^{6/7}}\]
\[dx = \frac{1}{7a^{6/7}}dz\]

Answer 19

\[\int\frac{1}{7a^{6/7}(1+a)}da\] is that workable?

Answer 20

I think we could int by parts now

Answer 21

I don't know, I've never done sometihng like this but I have a=7a^6/7, could this lead to an answer?

Answer 22

cant really say fer sure. Ive never tried it out b4 either :) still leafing thru some pages tho

Answer 23

I think the questions are bogus, e^(-x/2) involves an error function which we havent learned yet, and the answer for 1/(1+x^7) is humongus

Answer 24

in other words, I think we are supposed to realize that these are unsolvable for us

Answer 25

thx for the help :)

Answer 26

yep; that right :)

my text says: "you should realize that no table is adequate for all integration problems. A simple example is \(\int\ e^{-x^2}\). No elementary function exists whose derivative is \(e^{-x^2}\); in such a case it is necessary to restort to approx. techniques.