`I=int_(0)^(pi/4)(tan x-x)*dx`

Evaluate the definite integrals int_(0)^((pi)/(4)tan x)dx

I=int_(0)^( pi/4)(tan^(-1)x)^(2)/(1+x^2)dx

int_(0)^( pi/4)tan^(3)dx

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

Evaluate the following : int_(0)^(pi//4) " tan x dx"

int_0^(pi/2)1/(1+tan^2x)dx

Show that (i) int_(0)^(pi//2)f(sinx) d x=int_(0)^(pi//2)f(cos x) d x (ii) int_(0)^(pi//2)f(tan x) d x=int_(0)^(pi//2)f(cot x) d x (iii) int_(0)^(pi//2)f(sin 2 x) sin xd x = int_(o)^(pi//2)f(sin 2x).cosx d x

Evaluate : int_(0)^(pi//4) tan ^(2) x dx

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)

If l_(n)=int_(0)^(pi//4) tan^(n)x dx, n in N "then" I_(n+2)+I_(n) equals