Evaluate: `int(1n(1nx))/(x1nx)dx ,(x >0)`

Evaluate: int((1+1nx)^(5))/(x)dx

Evaluate: int a^(mx)b^(nx)dx

int(dx)/(1-cos nx)

Evaluate : (i) int_(0)^(1)x(1-x)^(n)dx (ii) int_(0)^(1)x(1-x)^(3//2)dx

Evaluate: int e^(x)(1+nx^(n-1)-x^(2n))/((1-x^(n))sqrt(1-x^(2n)))dx

Assuming that the interchange of limit and integration is permissible,the value of lim_(n rarr oo)int_(0)^(1)(nx^(n-1))/(1+x)dx;^(@)0

The value of int_(0)^(pi//2n) (1)/(1+cos nx)dx , is

What is int (l nx)/(x) dx equal to ?