24_(0)(1)int(dx)/(x(x^(n)+1))

int(1)/(x(x^(n)+1))dx

int dx/(x^n(1+x^n)^(1/n)) is

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

Evaluate the following integrals: int_(0)^(1)(24x^(3))/((1+x^(2))^(4))dx

int(dx)/(x^(n)(1+x^(n))^((1)/(n)))

int (x^(24)dx)/(x^(10)+1)

Let m,n be two positive real numbers and define f(n)=int_(0)^(oo)x^(n-1)e^(-x)dx and g(m,n)=int_(0)^(1)x^(m-1)(1-x)^(n-1)dx . It is known that f(n) for n gt 0 is finite and g(m, n) = g(n, m) for m, n gt 0 . int_(0)^(1)(x^(m-1)+x^(n-1))/((1+x)^(m+n))dx=

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