Integral of 1/(x^6+1) [Very tricky and Difficult Fun Integral]

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1) He is incredibly narcissistic and promotes himself shamelessly.
2) He misleads and confuses.
3) He pushes people away from Jesus Christ God, the Holy Trinity, the one and only messiah. White Jesus does all three of the above and more -- matching the ways of Satan.

Statues of Christ are equally offensive to God the Christ. While money is the biggest idol, Jesus spoke sufficiently against carved images.
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You can also find me on Tik Tok @reuslovesmath and @polarpiny

Here is another very fun integral:
In this video, I do a very interesting and very challenging Integral. There are many tricky parts but this is a fun integral of 1/x^6+1. This is one of the Most Difficult Calculus Problems.

[cemsentin]

My way is the simplest method for calculating this integral,

Int[dx/(x^6+1)]

=1/2*Int[2dx/(x^6+1)]

[ernestschoenmakers]

If one combines the arctangent terms and natural logarithm terms you'll get:
I = +
+ C.

[nullplan]

11:30 You know, you could just complete the square. Then the term to replace will be obvious. In this case x² + sqrt(3)x + 1 = (x + sqrt(3)/2)² + 1/4. So substitute u = x + sqrt(3)/2.

[davidavoryie]

Please what about you just do it t this way


Integral (x +1) power -1


And continue with substitution for the x+1 then solve

Will it be accepted as correct?

[jorgebilicparedesquispe]

Te confundiste en el signo, en la última integral, debería ir con -1/3

[spaghetti]

You made a mistake right after the partial fraction decomposition. When substituting E and F into the last integral, the negative sign of E was placed in front of the integral and you didn't compensate for that by making the one-third negative.

[pracheekesharwani]

Int[dx/(x^6+1)]
=Int[dx/{(x^3)*2+1*2}
=Tan*-1(x*3)+c

It's that right???

[jordanberman]

what program do you use to make these vids?