Alan G. answered 03/31/16
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Kenneth is correct. You need to put the dx at the end of the problem, even though it seems unnecessary. It is a needed part of the notation. This become especially important in third semester of calculus, when you do integrals with more than one variable.
Having said this, your integral seems to be non-elementary, which means it probably cannot be done with the standard techniques you use in a three-semester calculus course.
I say probably, because a well-known symbolic integration program could not do this integral. This means it is most likely not doable and certainly not easy even if it is doable.
May I ask where you got this problem? Is the logarithm base 10 or base e?