when your calculus test has only one problem

Here's a beautiful all-in-one calculus question for you guys! Of course, it includes a limit, an integral, a power series, and a second derivative! Here's Laplace's way of solving the Gaussian integral:    • how Laplace solved the Gaussian integral  
tanh^-1(x), inverse hyperbolic tangent in terms of logarithm    • Inverse tanh(x)  

Previously:
all-in-one calculus question ep1.    • my all-in-one calculus question  
all-in-one calculus question ep2.    • my all-in-one calculus question (uncut)  

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