If `int_(n)=int_(-pi)^(pi)(sin nx)/((1+pi^(x))sinx) dx, n=0,1,2,……….` then

If I_n=int_(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... then which one of the following is not true ?

int_(0)^(pi/2) (sinx)/(1+cos^(2)x)dx

int_(0)^( pi)(dx)/(1+sin x)

int_(0)^(pi//2)sinx sin2x sin3x sin 4x dx=

Evaluate: int_(-pi/2)^(2pi)sin^(-1)(sinx)dx

If I_n = int_0^(pi/2) (sin^2 nx)/(sin^2 x) dx , then

Evaluate int_(0)^(pi)(sin 6x)/(sinx) dx .

int_(0)^(pi)(x)/(1+sinx)dx .

If I _(n)=int _(0)^(pi) (sin (2nx))/(sin 2x)dx, then the value of I _( n +(1)/(2)) is equal to (n in I) :

int_(-pi)^(pi) ( e^(sin x ))/( e^(sinx) + e^(-sinx))dx is equal to