How can I expand (1+x)^n, where n is a posive integer number?

I want to find the edges b and c of the triangle ABC knowing that the mesure of angles are 15 degrees, 30 degrees and 135 degrees and the length of one side is 3. I tried

restart:

a:=3:

eq1:=(a^2+b^2-c^2)/(2*a*b):

eq2:=(b^2+c^2-a^2)/(2*b*c):

eq3:=(c^2+a^2-b^2)/(2*a*c):

solve([eq1=cos(15*Pi/180),eq2=cos(30*Pi/180),eq3=cos(135*Pi/180)],[c,b]);

I want to solve the equation (1 + 1/x)*(1 + 1/y)*(1 + 1/z)=2 with integer solutions. I tried 

isolve((1 + 1/x)*(1 + 1/y)*(1 + 1/z)=2);

and I get {x = -1, y = -2, z = 0}. Is this a bug?

How to solve this inequality? 6/(2*x+1)>(1+log[2](2+x)/x). I tried

solve(6/(2*x+1)>(1+log[2](2+x)/x),x);

I receive: "Warning, solutions may have been lost."

When I input int(sin(x)^4,x); I received -1/4*sin(x)^3*cos(x)-3/8*cos(x)*sin(x)+3/8*x. How do I receive 3*x/8 + 1/4*sin(2*x)+1/32*sin(4*x)?