`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`

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 I_(n)=int_(0)^(pi//4)tan^(n)x dx , where n ge 2 , then : I_(n-2)+I_(n)=

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

If I_n=int_0^ooe^(-x)x^(n-1)log_exdx , then prove that I_(n+2)-(2n+1)I_(n+1)+n^2I_n=0

If I_(n)=int_(0)^(1)x^(n)e^(-x)dx for n in N, then I_(7)-I_(6)=

If I_(n)=int_(0)^(pi/2) sin^(x)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(x^(n)dx)/(sqrt(x^(2)+a)) then prove that I_(n)+(n-1)/(n)al_(n-2)=(1)/(n)x^(n-1)*sqrt(x^(2)+a)

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

If = int_(0)^(1) x^(n)e^(-x)dx "for" n in N "then" I_(n)-nI_(n-1)=

IfI_n=int_x^pix^nsinx dx ,t h e n fin d t h e v a l u eof I_5+20 I_3dot