integration: sqrt(arctan(x)) = ?

[cAsk]

integration: sqrt(arctan(x)) = ?

 

[stapel]

integration: sqrt(arctan(x)) = ?

Please reply with a clear listing of your thoughts and efforts so far, so we can see where you're getting bogged down. Thank you!

 

[Deleted member 4993]

integration: sqrt(arctan(x)) = ?

\(\displaystyle \displaystyle{\int \sqrt {\tan^{-1}(x)} dx}\)

substitute:

tan^-1(x) = u → x = tan(u)

dx = sec²(u) du

Then:

\(\displaystyle \displaystyle{\int \sqrt {\tan^{-1}(x)} \ dx}\)

\(\displaystyle = \ \displaystyle{\int \sqrt {u} \ * \ \sec^2(u) \ du}\)

Continue....

 

[cAsk]

\(\displaystyle \displaystyle{\int \sqrt {\tan^{-1}(x)} dx}\)

substitute:

tan^-1(x) = u → x = tan(u)

dx = sec²(u) du

Then:

\(\displaystyle \displaystyle{\int \sqrt {\tan^{-1}(x)} \ dx}\)

\(\displaystyle = \ \displaystyle{\int \sqrt {u} \ * \ \sec^2(u) \ du}\)

Continue....

thanks!