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

1.	Evaluate the following integral: `int_0^1(sqrt(tan^(-1)x))/(1+x^2)dx`
Answer» 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)` `= 2/3 xx 1/8 xx (pi)^(3/2)` `= (pi)^(3/2)/12` Answer

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