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The integral given is: $$\int_{0}^{1}\big\lbrace\frac{1}{x}\big\rbrace \big\lbrace\frac{1}{1-x}\big\rbrace \big\lbrace1-\frac{1}{x}\big\rbrace dx$$ where $\big\lbrace x\big\rbrace$ represents the fractional part of $x$

I first tried breaking it using a piecewise definition but I couldn't figure out how to do it as there wasn't any consistent pattern that I could spot.

I tried graphing it to get an idea but that also didn't get me anywhere.

Finally, I tried using the property of definite integral that $\int_{0}^{a}f(x)dx=\int_{0}^{a}f(a-x)dx$ but the first and seccond terms remained the same and the last term changed but not it did not lead to any noticeable changes.

I am stuck now. Any help would be appreciated.

Answers