Question

Anyone calculus here?
Integrate 2pi(1/x)*sqrt(1 + 1/(x^4))?

Answer 1

So to solve this question make the equation easier to solve
(2(pi))/x + 2(pi)x^-4)/x
= (2(pi))/x + 2(pi)x^-5
integrate function
Use log rule for first fraction
integral of 2(pi)/x = 2(pi)logx
Then integrate normally with second fraction
integral of 2(pi)x^-5= 2(pi)x^-4/-4
Add both integrals, therefore the final solution is;
2(pi)logx - (pi)/2x^4

Answer 2

Also just in case you didn't notice or know about. I moved the x up to the numerator by make the power a negative e.g 1/x^4 = x^-4
Also x^-4/x = x^-5

Answer 3

It's a long process..... i was tired....!! good question though

Answer 4

you didn't consider sqrt ?
\(\sqrt {1+1/x^4}\)

Answer 5

yeah i checked that...

Answer 6

i don't think that function can be integrated in terms of standard functions
where did u get this question from ?

Answer 7

it's an old IIT question.... !!

Answer 8

hmm, i can think of a substitution
\(\Large 1/x^2 = u \)
need to work it out to check whether it works

Answer 9

I thought same at first instance but it can be integrated...

Answer 10

Check by part, there's a bit of work required here I guess

Answer 11

That's all i can get.. please verify if there's a mistake or need further calculation.

Answer 12

More you can try u substitution for the entire root thingy. It should work nice I guess

Answer 13

calculation is lengthy enough..and after understanding it..it's hell lot of work.

Answer 14

Well you won't have that much of work compared to by parts

Answer 15

ok i will try.. thanks!

Answer 16

Anytime