Probability and Probability Density

For a one dimensional problem (variable = x), obtain a formula for the probability density (P(x)) of the described particle if the total range (domain) of x is a<=x<=b where a<b (a and b > 0), assuming the wave function over this domain is A/x^1/2 ( = A/sqrt(x)). Remember that P(x)dx is the probability of finding the particle within dx of x. (see Dykstra's 'Physical Chemistry, A Modern Introduction', page 274.)
Use the single letters `A', `a', 'x' and `b' in your answer and `log()' for the natural log. Multiplication signs must be indicated properly.
Answer is:

Query, is the above formula correct?