`xe^(x)(-1)/(x)`

int_(0)^(1)(xe^(x))/((x+1)^(2))dx

int_(0)^(1)(xe^(x))/((x+1)^(2))dx=

If f(x)={xe^(-[(1)/(|x|)+(1)/(x)]);x!=0;0;x=0 Prove that f(x) is not differentiable at x=0

f(x) ={{:( xe ^(-((1)/(x)+(1)/(|x|))), x ne 0),( a , x=0):} the value of a , such that f(x) is differentiable at x=0, is equal to

Let f(x)=(xe)^((1)/(|x|)+(1)/(x));x!=0,f(0)=0, test the continuity & differentiability at x=0