Evaluate `int cosmx cosnx dx` where `m,n` are positive integers, `m!=n` What happens if `m=n?`

Evaluate int cosmx cosnx dx , where m,n are positive integers and m ne n . What happens if m=n?

Evaluate int sinmx sin nx dx , where m and n are positive integers. What happens if m=n?

n|sin x|=m|cos|in[0,2 pi] where n>m and are positive integers

If m!=n where m,n are positive integers,then int sin mx sin nxdx=

Evaluate the integerals. f cos mx cos nx dx on R, m ne n, m and n are positive integers.

Evaluate int_(0)^(infty)(x^(n))/(n^(x)) dx, where n is a positive integer.

If (m)=64, where m and n are positive integers,find the value of n)^(mn)..

Evaluate the following integrals: intsin mx cos nx dx where m and n are distinct positive integers.

In a triangle ABC , if (b+c) / 11 = (c+a) / 12 = (a+b) / 13 then cosA / l = cosB / m = cosC / n where l, m, n are least positive integer. Find the value of (l+m+n) .