[" Let "I_(n)=int_(0)^( pi/4)tan^(n)xdx" ,then "],[(1)/(I_(2)+I_(4)),(1)/(I_(3)+I_(5)),(1)/(I_(4)+I_(6)),(1)/(I_(5)+I_(7))" ,form an: "]

int_(0)^(pi//4)2tan^(3)xdx

If I_(n)=int_(0)^(pi//4)tan^(n)xdx , then (1)/(I_(3)+I_(5)) is

let I_(n)=int_(0)^((pi)/(4))tan^(n)xdx,n>1

int_0^(pi/4) tan^(2)xdx

int_(0)^((pi)/(4))tan^(2)xdx

If I_(n)=int_(0)^( pi/4)tan^(n)xdx, show that (1)/(I_(2)+I_(4)),(1)/(I_(3)+I_(5)),(1)/(I_(4)+I_(6)),(1)/(I_(5)+I_(7)),... form an A.P. Find the common difference of this progression.

If I_(n) = int_(0)^(pi//4) tan^(n) x dx then (1)/(I_(3)+I_(5))=

"int_(0)^( pi/2)cos^(n)xdx

Let I_(n)=int_(0)^(pi//4)tan^(n)xdx,n in N , Then

int_(0)^((pi)/(4))tan^(4)xdx=