Very Difficult Integration by Parts - Integral of Artan(x)/(1+(1/x^2))

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Here is another really fun integral:

In this video, I do a very fun challenging double integration by parts problem.

[DrLiangMath]

By the way, the third term should be negative. Other than that, excellent!

[arnabdas_]

X tan^-1(X) - 0.5 ln(X^2+1) - 0.5[tan^-1(X)]^2

minus before the term with ln

[piyalichoudhury]

This one is a very complicated method... Just substitute arctan(x) for t and it's done at once...

[PunmasterSTP]

As others have pointed out, you could just make the substitution u = arctan(x), but this was still a cool video! 👍

[KelfranGt]

The ln doesn’t need absolute value cuz the inside is always positive

[tomsalmon]

Wouldn't it have just been much easier for the last integration by parts to just let u=tan^-1(x)=u then du=dx/(x^2+1)as you did then simply substitute u in giving integral of u, giving u^2/2, then just subbing tan^-1(x) back in for u?

[rohitpramanik]

I am done it. This intregal answer is : xtan^-1(x)-1/2 log|1+x²| -1/2 {tan^-1(x)}²

[gaunterodimm]

You call it advanced calculus???

Take the lcm and get integral as
x^2 arctanx /1+x^2
Substitute arctanx = t then
dx/1+x^2 = dt and x =tan^2t

Integral reduces to
t tan^2t dt simply apply integration by parts by assuming t as 1st function and tan^2t as 2nd you get your answer

[sabbirahmad]

Actually the question is : integration of (tanx)^3 (sinx)^0.5 dx

[ritilranjan]

Why not directly substitute tan inverse x as y? That way it will simply become integration of
sec²y cosec²y which is very easy

[jackhounsom]

the answer should be -1/2ln|1+x^2| not +

[cristofer]

is little funny, pude hacerlo escribiendolo en un....em, ...I was able to do it by writing it in a comment. Doing it mentally is difficult, remembering everything, but with practice and mental clarity you can.It is not so difficult when one knows the formulas well. This is a good rola (rola=good song)

[Ridhimagarg]

This can also be done by integration by parts method .It would be done at once.

[DrLiangMath]

Interesting problem and excellent explanation!

[lich]

Excelent video. Someone knows the method for integrals with several sin and cos functions where variable x is changed for tan(t/2) (or something like that, i dont remember clearly)?

[Love_Sinha]

What if, we use that x^2 ±1 trick in the second step itself and then separate ?
My answer seems to be xtan^-1x + tan^-1x - x -{(tan^-1x)^2}/2
Anybody with the same answer ?

[sabbirahmad]

what of the solution of this problem: integration of (tanx)power 3 root sinx dx

[lightness]

You could also have U subbed for A right? Plz correct me if wrong i want to know

[prerakcontractor]

Why are the coeffecients of ln|x^2+1| different in ur answer and the answer u popped?

[nicogehren]

beautiful solution sir thank u keep it up thank