prove that lnx differentiated is 1/x

Shower-cleaner liquid is sold in spray bottles. The volume of liquid in a bottle may be modelled by a normal distribution with mean 955 ml and a standard deviation of 5 ml. Determine the probability that the volume in a particular bottle is:

What is the indefinite integral of xlog(x)?

The Volume of a tin of radius r cm is given by V=pi*(40r-r^2-r^3). Find the positive value of r for which dV/dr=0 and find the value of V for this r.

How would I go about drawing the graph of f(x) = sin(x)/(e^x) for -π≤x≤2π?