[" 53.) "u_(n)=int_(0)^((pi)/(4))tan^(n)xdx" रक्ञ GFाड कर,"],[qquad u_(n)+u_(n-2)=(1)/(n-1)(n>1)]

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

If u_(n)=int_(0)^((pi)/(4))tan^(n)xdx , show that, u_(n)+u_(n-2)=(1)/(n-1)(ngt1) , hence find u_(5)

I_(n)=int_(0)^((pi)/(4))tan^(n)xdx, then the value of n(l_(n-1)+I_(n+1)) is

If I_(n)=int_(0)^( pi/4)tan^(n)xdx, prove that I_(n)+I_(n-2)=(1)/(n+1)

If u_(n)=int_(0)^((pi)/(2))theta sin^(n)theta d theta and n>=1, then prove that u_(n)=((n-1)/(n))u_(n-2)+(1)/(n^(2))

If u_(n)=int_(0)^((pi)/(2))x^(n)sin xdx then u_(10)+90u_(8) is equal to

If U_(n) = int_0^(pi/4) tan^(n) x dx then u_(n)+u_(n-2) =

If v_n=int_0^1x^n tan^-1xdx , show that: (n+1)u_n+(n-1)u_(n-2)=pi/2-1/n

If y^(2)=ax^(2)+2bx+c and u_(n)= int (x^(n))/(y)dx , prove that (n+1)a u_(n+1)+(2n+1)bu_(n)+(n)c u_(n-1)=x^(n)y and deduce that au_(1)=y-b u_(0), 2a^(2)u_(2)=y(ax-3b)-(ac-3b^(2))u_(0) .