सिद्ध कीजिये -
(b) `int_(0)^(pi//2)(sqrtcotx)/(sqrtcotx+sqrttanx)dx=(pi)/(4)`

int_0^(pi//2)(sqrttanx+sqrtcotx)dx

Integrate: int_0^(pi/2)(sqrttanx)/(sqrttanx+sqrtcotx)dx

int_0^(pi/2) (sqrtcotx)/(sqrttanx+sqrtcotx) dx is equal to :

int_(pi/6)^(pi/3) (dx)/(1+sqrtcotx) =

int_(pi//6)^(pi//3)dx/(1+sqrtcotx)

int_(0)^(pi//2)(cos^(4)x)/((sin^(4)x+cos^(4)x))dx=(pi)/(4)

int(sqrttanx+sqrtcotx)dx

I : int_(0)^(pi//2)(sqrtcotx)/(sqrt(tanx)+sqrt(cotx))dx=(pi)/(4) II : int_(0)^(pi//2)(2sinx+3cosx)/(sinx+cosx)dx=(pi)/(4)

int_(0)^(pi//2)(dx)/((1+sqrt(tanx)))=(pi)/(4)