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 I_3+I_5 is

If I_(n)=int_(0)^((pi)/(4)) tan^(n)x dx , then the value of lim_(n to oo) n(I_(n)+I_(n-2)) is -

If I_(n)=int_(0)^(pi/2) sin^(n)x dx , then show that I_(n)=((n-1)n)I_(n-2) . Hence prove that I_(n)={(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(1/2)(pi)/2,"if",n"is even"),(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(2/3)1,"if",n"is odd"):}

If I_(n)=int_(0)^(pi//4) tan^(n)x dx, (ngt1 is an integer ), then (a) I_(n)+I_(n-2)=1/(n+1) (b) I_(n)+I_(n-2)=1/(n-1) (c) I_(2)+I_(4),I_(6),……. are in H.P. (d) 1/(2(n+1))ltI_(n)lt1/(2(n-1))

IfI_(m , n)=int_0^(pi/2)sin^m xcos^n xdx , Then show that I_(m , n)=(m-1)/(m+n)I_(m-2,n)(m ,n in N) Hence, prove that I_(m , n)=f(x)={((n-1)(n-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))pi/4 when both m and n are even ((m-1)(m-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))}

If I_(n)=int sin^(n)x dx , show that, I_(n)=-(1)/(n) sin^(n-1)x cosx+(n-1)/(n).I_(n-2) . Hence, evaluate, int sin^(6)x dx .

if I_n=int_0^(pi/4)tan^ntheta.d theta,then n in N,n(I_(n-1)+I_(n+1)) equals

If I_n = int tan^n x dx , then prove that I_n = (tan^(n-1) x)/(n - 1) - I_(n - 2) . Hence find int tan^7 x dx

If I_(n)=int_(0)^((pi)/(4))tan^(n)thetad theta , for any positive integer n, then the value of n(I_(n-1)+I_(n+1)) is -

IfI_n=int_0^1x^n(tan^(-1)x)dx ,t h e np rov et h a t (n+1)I_n+(n-1)I_(n-2)=-1/n+pi/2