Question

Evaluate the integral.

integral of xdx/(x^4 + X^2 + 1)

Answer 1

it doesn't make sense ! do u want integral for the x^4.....part ?!

Answer 2

http://integrals.wolfram.com/index.jsp

Answer 3

did that help !?

Answer 4

No, it is suppose to be the integral of the whole thing... It is suppose to be solved with substitution, integration by parts, and/or partial fractions... but i cant figure out how to do it

Answer 5

oh i got it its basically this x/(x^4 + X^2 + 1) plug that in that site

Answer 6

did u get the answer for it !?

Answer 7

Yes, that is what it is....But do you know how to solve it....I need to show work.

Answer 8

First make a substitution u = x^2. Then you will have the integral wrt u of
1/2 . 1/(u^2 + u + 1)

Now note that u^2 + u + 1 = (u + 1/2)^2 + (sqrt(3)/2)^2

So you will need to make now another substitution u = something .... and hopefully you know what it is.

Answer 9

Would the second substitution be v=u+1/2?

Answer 10

Well, you could do that

But let me ask you this. Suppose you had to evaluate this indefinite integral: what substitution would you use?

\[\int\limits \frac{1}{1+t^2} \ dt\]

Answer 11

Ok, I get it now... the arctan would be used. Thank you for your help.

Answer 12

Yep