Evaluate: for `m in N ,` `intx^(3m)+x^(2n)+x^m)(2x^(2m)+3x^m+6)^(1/m)dx ,x >0`

Evaluate: inta^(m x)b^(n x)dx

If m is a non-zero number and int (x^(5m-1)+2x^(4m-1))/(x^(2m)+x^m+1)^3 dx=f(x)+c , then f(x) is:

Find the L.C.M of x^(3) + x^(2) - x - 1 and x^(3) + 3x^(2) - x - 3

A function f is defined by f(x)=|x|^m|x-1|^nAAx in Rdot The local maximum value of the function is (m ,n in N), 1 (b) m^nn^m (m^m n^n)/((m+n)^(m+n)) (d) ((m n)^(m n))/((m+n)^(m+n))

If x^(m)y^(n) = (x+y)^(m+n),find dy/dx.

If int(m^((1)/(x)))/(x^(2))dx=k(m^((1)/(x)))+c then k is:

Find a negative value of m if the Co-effcient of x^(2) in the expanion of (1 + x)^(m) , |x| lt 1 is 6 .

The number of integral values of m for which the equation (1+m^(2))x^(2)-2(1+3m)x+(1+8m)=0, has no real roots is

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=