# Sunday Afternoon Maths LIII

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## Tags

time geometry 2d shapes 3d shapes numbers spheres trigonometry complex numbers algebra lines graphs coordinates odd numbers fractions differentiation calculus folding tube maps ellipses triangle numbers money bases triangles squares area square numbers chess probability circles averages speed sport multiples dates factors parabolas functions logic cards games people maths shape prime numbers irreducible numbers probabilty angles proportion dice integration sum to infinity dodecagons hexagons multiplication factorials coins shapes regular shapes colouring grids floors integers rugby crosswords percentages digits sums christmas rectangles clocks menace routes taxicab geometry remainders chalkdust crossnumber palindromes sequences means unit fractions division square roots surds doubling quadratics indices planes volume number partitions ave pascal's triangle mean advent symmetry arrows addition cube numbers star numbers perfect numbers**Posted on 2016-05-29**

## An Integral

Source: Alex Bolton (inspired by Book Proofs blog)

What is

$$\int_0^{\frac\pi2}\frac1{1+\tan^a(x)}\,dx?$$
## Lots of Ones

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

If you enjoyed this puzzle, check out Sunday Afternoon Maths LXII,

puzzles about people maths, or a random puzzle.

puzzles about people maths, or a random puzzle.