What makes you believe that this function has an antiderivative that can be expressed in terms of not only elementary functions (in the technical sense of the term) of the various non-elementary functions that Mathematica knows about?

Would numerical integration over some prescribed interval of values of r suffice for your purposes? If so, then for specific number a and b you want to use

 NIntegrate[A B, {r, a, b}]

You have several fundamental Mathematica syntax errors in the code you show, along with unnecessary parentheses and multiplication signs.

Recall that in Mathematica:

• built-in names begin with upper-case letters, so you should, if possible, avoid those when naming things;

• the base of natural logs is denoted by E, not e (although a vaguely similar stylized lower-case version is available); and

• functions use square brackets [...] rather than parentheses to enclose their arguments.

Thus to start to correct things:

    A = ArcCos[(r^2 + v^2 - d^2)/(2 v r)]
    B = (2 L r)/(1 + (r^E)/z)

Now try the integration:

     Integrate[A B, r]

Unfortunately, Mathematica just returns as output a formatted result (with an integral sign) of the input, meaning it does not know how to integrate this as a function of r.