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This requires your knowledge of integration by parts. The trick here is that lnx can also be written as lnx*1 (as any term multiplied by 1 is itself). We set u=lnx and dv/dx equal to 1. Hence from this we...

The problem can be easily solved using energy formulas. The only force that acts on the departing object is the gravitational force, which is conservative. Therefore the total energy is conserved on the t...