int_(0)^(1)(log(1+n))/(1+n^(2))dn

int_(0)^(1)(log(1)/(x))^(n-1)dx equals

sum_(n=1)^(oo)(1)/(n^(2))=(pi^(2))/(6) and int_(0)^(1)(ln x)/(1-x^(2))dx=-(pi^(2))/(lambda)

Evaluate int_(0)^(1)((log(1/x))^(n-1)dx .

Evaluate int_(0)^(1)((log(1/x))^(n-1)dx .

Evaluate int_(0)^(1)((log(1/x))^(n-1)dx .

Evaluate int_(0)^(1)((log1)/(x))^(n-1)dx .

Let n in N such that n gt 1 . Statement-1: int_(oo)^(0) (1)/(1+x^(n))dx=int_(0)^(1) (1)/((1-x^(n))^(1//n))dx Statement-2: int_a^b f(x)dx=int_(a)^(b) f(a+b-x)dx

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)

int_ (2) ^ (3) (n) / (1 + n ^ (2)) dn