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Sunday Afternoon Maths LIII

 Posted on 2016-05-29 

Lots of ones

Is any of the numbers 11, 111, 1111, 11111, ... a square number?

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An integral

Source: Alex Bolton (inspired by Book Proofs blog)
What is
$$\int_0^{\frac\pi2}\frac1{1+\tan^a(x)}\,dx?$$

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If you enjoyed these puzzles, check out Sunday Afternoon Maths LXVII,
puzzles about 2d shapes, or a random puzzle.

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