The year when the open problem was proposed:

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It is an open problem to find an explicit formula for the indefinite integral $$ \int_{-\infty}^x \frac 1 {\sqrt{2 \pi}} e^{-y^2/2} \frac{\sin y - \cos y} {\log( 1 + y^2 + y^4)} dy.$$ Multiple attempts at integration by parts and substitution failed so far to generate an answer.