MHB How Do You Integrate $\int^1_0 \log^2(1-x) \log^2(x) \, dx$?

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Solve the following

$$\int^1_0 \log^2(1-x) \log^2(x) \, dx$$​
 
Last edited:
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Hint

$$\sum H_k x^k = -\frac{\log(1-x)}{1-x}$$
 

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