[int_(0)^(oo)(x^(n+1))/(x+1)dx],[f'x^(0)

int_(0)^(oo)(1)/(x+a)dx

int_(0)^(oo)(x)/(1+x^(4))dx=

int_(0)^(oo)(1)/(1+e^(x))dx=

int_(0)^(oo)(tan^(-1)x)/(1+x^(2))dx

int_(0)^(oo) (x)/(1-x)^(3//4)dx=

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-m)^(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)^(oo)(x^(m-1))/((1+x)^(m+n))dx=

If I(m,n)=int_(0)^(1)x^(m-1)(1-x)^(n-1)dx,(m,n in I,m,n>=0),th epsilonI(m,n)=int_(0)^(oo)(x^(m-1))/((1+x)^(m-n))dxI(m,n)=int_(0)^(oo)(x^(m-1))/((1+x)^(m+n))dxI(m,n)=int_(0)^(oo)(x^(n-1))/((1+x)^(m+n))dxI(m,n)=int_(0)^(oo)(x^(n))/((1+x)^(m+n))dx

int_(0)^(oo)(x)/((1+x)(1+x^(2)))dx

int_(0)^(oo)(dx)/((1+x)sqrt(x))