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)^(1)x^(n)(tan^(-1)x)dx, then prove that(n+1)I_(n)+(n-1)I_(n-2)=-(1)/(n)+(pi)/(2)

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)^(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_0^ooe^(-x)x^(n-1)log_exdx , then prove that I_(n+2)-(2n+1)I_(n+1)+n^2I_n=0

If l_(n)=intcos^(n)xdx, prove that l_(n)=(1)/(n)(cos^(n-1)xsinx)+((n-1)/(n))l_(n-2) .