imchadee Group Title integral of arctan sqrt of x dx 3 months ago 3 months ago

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1. myininaya

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

2. SithsAndGiggles

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