" 15."int_(0)^(1)(sqrt(tan^(-1)x))/(1+x^(2))dx

Evaluate the following : int_(0)^(1)(sqrt(tan^(-1)x))/(1+x^(2))dx.

int_(0)^(sqrt(3))tan^(-1)((2x)/(1-x^(2)))dx

int_(0)^(oo)((tan^(-1)x)/((1+x^(2))))dx

int_(0)^(1)(tan^(-1)x)/((1+x^(2)))dx

int_(0)^(1)(tan^(-1)x)/(1+x^(2))dx

int_(0)^(1)x(tan^(-1)x)^(2)dx

int_(0)^(1)tan ^(-1) (x/sqrt(1-x^(2)))dx=

int_(0)^(oo)(tan^(-1)x)/(1+x^(2))dx

int sqrt(tan^-1 x)/(1+x^2) dx

STATEMENT-1 : int_(0)^(oo)(dx)/(1+e^(x))=ln2-1 STATEMENT-2 : int_(0)^(oo)(sin(tan^(-1)))/(1+x^(2))dx=pi STATEMENT-3 : int_(0)^(pi^(2)//4)(sinsqrt(x))/(sqrt(x))dx=1