i need to prove that

sup $\displaystyle {(xsin(x))/(x+1) |x>0}}=1$

i succeded proving that 1 is an upper bound of $\displaystyle f(x)$

now i need to prove that 1 is the lowest upper bound. i tried to assume that there's another number (let called $\displaystyle c$), that is also an upper bound of $\displaystyle f(x)$ but is lower than 1.

$\displaystyle c<1$

but i don't really know how to go forward.. (Worried)

what can i do? i'm so suck in proving things...