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This paper will introduce two methods to calculate a quite complicated integral. This paper uses the answer of the former integral to calculate a more general integral which involves the arbitrary positive integer n. Back to the integral, the first method is quite traditional, the paper uses the property of the gamma function and the beta function. Through some basic transformations, this paper can induce it to the form, which uses some basic properties of this function to solve. The next method involves the residue formula. This paper will solve this problem in the complex plane and will select a suitable contour to solve this problem. To accomplish this task, it is also necessary to calculate the residue and use residue formula. Then it is not hard for us to generalize this proposition to an arbitrary positive integer n by a series of transformations. This paper wants to investigate this question in a totally different way, and show an accessible way to associate this powerful formula with the calculation of the integral.
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