Evaluate the following integral: `int_0^1(sqrt(tan^(-1)x))/(1+x^2)dx`

Explanation

let `y= tan^-1 x`

`dy/dx = 1/(1+x^2)`

when `x=0, y=0`

`x=1, y= pi/4`

`int_0^(pi/4) sqrt y dy`

`2/3[y^(3/2)]_0^(pi/4)`

`2/3(pi/4)^(3/2)`

`= 2/3 xx 1/4^(2/3) xx (pi)^(3/2)`

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