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 126 Is there a symbol for “taking a derivative of something”? 91 Can sum of a rational number and its reciprocal be an integer? 40 Unexpected examples of natural logarithm 25 Find the probability that the thirteenth spade will appear before the thirteenth diamond? 18 An astounding identity: $\int_0^{\pi/2}\ln\lvert\sin(mx)\rvert\cdot \ln\lvert\sin(nx)\rvert\, dx$

### Reputation (20,678)

 +25 Seeking Methods to solve $I = \int_{0}^{\frac{\pi}{2}} \frac{\arctan\left(\sin(x)\right)}{\sin(x)}\:dx$ +35 Difficult variation of the committee problem +20 Can I prove there is no real solution except $x=0, x=1$, without using the function $W(x)$? +10 Find a matrix B such that $B^5 = A$

### Questions (191)

 201 “Integral Milking” 77 Do numbers get worse than transcendental? 61 Find three non-constant, pairwise unequal functions $f,g,h:\mathbb R\to \mathbb R$… 47 What numbers can be created by $1-x^2$ and $x/2$? 33 Painting the plane, and finding points one unit apart

### Tags (275)

 315 calculus × 75 127 integration × 62 194 algebra-precalculus × 40 126 notation × 3 174 sequences-and-series × 75 108 elementary-number-theory × 15 152 derivatives × 20 103 integers × 6 130 number-theory × 22 93 definite-integrals × 48

### Accounts (13)

 Mathematics 20,678 rep 638104 Puzzling 679 rep 117 Area 51 371 rep 9 Philosophy 163 rep 16 Writing 133 rep 3