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int(pi//6)^(pi//3)(1)/((1+sqrt(tanx)))dx...

`int_(pi//6)^(pi//3)(1)/((1+sqrt(tanx)))dx=(pi)/(12)`

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To solve the integral \[ I = \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{1}{1 + \sqrt{\tan x}} \, dx \] we will use a property of definite integrals and some trigonometric identities. ...
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Statement-1: The value of the integral int_(pi//6)^(pi//3) (1)/(sqrt(tan)x)dx is equal to (pi)/(6) Statement-2: int_(a)^(b) f(x)dx=int_(a)^(b) f(a+b-x)dx

I_(1) = int_(pi/6)^(pi/3) (dx)/(1+sqrt(tanx)) and I_(2) = (sqrt(sinx)dx)/(sqrt(sinx) + sqrt(cosx)) What is I_(1) equal to ?