int_(0)^(int(1)/(1+tan n))dx

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

Let I_(n) = int_(0)^(1)x^(n)(tan^(1)x)dx, n in N , then

Let n in N such that n gt 1 . Statement-1: int_(oo)^(0) (1)/(1+x^(n))dx=int_(0)^(1) (1)/((1-x^(n))^(1//n))dx Statement-2: int_a^b f(x)dx=int_(a)^(b) f(a+b-x)dx

int _(0)^(1) (tan ^(-1))/(x ) dx =

Let int_(0)^(1)tan^(-1)((tan x)/(2))dx=alpha then int_(0)^(1)tan^(-1)((tan x-2cot x)/(3))dx is

int_(0)^(pi//2n)(dx)/(1+(tan nx)^(n)) is equal to n in N :

int_(0)^(pi//2n)(dx)/(1+(tan nx)^(n)) is equal to n in N :

I_(n)=int_(0)^(pi//4) tan^(n)x dx , where n in N Statement-1: int_(0)^(pi//4) tan^(4)x dx=(3pi-8)/(12) Statement-2: I_(n)+I_(n-2)=(1)/(n-1)

I_(n)=int_(0)^(pi//4) tan^(n)x dx , where n in N Statement-1: int_(0)^(pi//4) tan^(4)x dx=(3pi-8)/(12) Statement-2: I_(n)+I_(n-2)=(1)/(n-1)