anonymous
  • anonymous
integral of arctan sqrt of x dx
Mathematics
jamiebookeater
  • jamiebookeater
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myininaya
  • 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
anonymous
  • anonymous
An only slight different substitution:\[u=\sqrt x~~\Rightarrow~~du=\frac{dx}{2\sqrt x}~~\Rightarrow~~2u~du=dx\] So \[\int\tan^{-1}\sqrt x~dx=2\int u\tan^{-1}u~du\]

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