If `I_n=intdx/(x^2+a^2)^n,ninN`, then show that: `I_(n+1)=1/(2na^2)x/((x^2+a^2)^n)+(2n-1)/(2n). 1/a^2I_n`

If I_n=int_0^1(dx)/((1+x^2)^n); n in N , then prove that 2nI_(n+1)=2^(-n)+(2n-1)I_n

If I_n=int_0^1(dx)/((1+x^2)^n); n in N , then prove that 2nI_(n+1)=2^(-n)+(2n-1)I_n

If I_n=int x^nsqrt(a^2-x^2)dx, prove that I_n=-(x^(n-1)(a^2-x^2)^(3/2))/((n+2))+((n+1))/((n+2))a^2I_(n-2)

If I_n=intsqrt((a^2+x^2)^n)dx , Prove that: I_n=(xsqrt((a^2+x^2))^n)/(n+1)+(na^2)/(n+1)int(a^2+x^2)^(n/2-1)dx

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"):}

intdx/(xsqrt(x^(2n)-a^(2n)))

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=intxcos^nxdx,prove that: I_n=1/n cos^(n-1)x(sinx)+(n-1)/(n)I_(n-2)

If I_(n)=int cos^(n)x dx . Prove that I_(n)=(1)/(n)(cos^(n-1)x sinx)+((n-1)/(n))I_(n-2) .

If I_n=int_0^(pi//4)tan^("n")x dx , prove that I_n+I_(n-2)=1/(n-1)dot