Question

integral of arctan sqrt of x dx

Answer 1

hey
try letting u=arctan(sqrt(x))
then write it as tan(u)=sqrt(x)
then write it as tan^2(u)=x
then find the derivative


then you will need integration by parts

Answer 2

An only slight different substitution:\[u=\sqrt x~~\Rightarrow~~du=\frac{dx}{2\sqrt x}~~\Rightarrow~~2u~du=dx\]
So
\[\int\tan^{-1}\sqrt x~dx=2\int u\tan^{-1}u~du\]