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نشان دهید: $$ \int _0^1 (Arctanhx)^{n} dx= \frac{ \Gamma (n+1)}{ 2^{2n-1} }. \xi (n)[ 2^{n} -2] \leadsto \int _0^1 Arctanh ^{n} xdx= \int _0^1 [ \frac{1}{2}ln | \frac{1+x}{1-x} | ]^{n} dx$$

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پاسخ در لینک زیر:
https://s9.uupload.ir/files/mansour4887/Doc2.pdf?download