Aryabhata
Reputation
56,743
397/400 score
4 120 211
Impact
~1.1m people reached

• 97 helpful flags
• 8,174 votes cast

 124 Solving the integral $\int_{0}^{\infty} \frac{\sin{x}}{x} \ dx = \frac{\pi}{2}$? 76 Comparing $\pi^{e}$ and $e^{\pi}$ 56 Which one result in mathematics has surprised you the most? 53 Root Calculation by Hand 49 Calculating the integral $\int_{0}^{\infty} \frac{\cos x}{1+x^2}\mathrm{d}x$ without using complex analysis

### Reputation (56,743)

 +10 Solve the functional equation $f (x+y)=f (x)+f (y)+xy (x+y)$, $f$ continuous at $0$ +10 Comparing $\pi^{e}$ and $e^{\pi}$ +10 Calculating the integral $\int_{0}^{\infty} \frac{\cos x}{1+x^2}\mathrm{d}x$ without using complex analysis +10 Solving the integral $\int_{0}^{\infty} \frac{\sin{x}}{x} \ dx = \frac{\pi}{2}$?

### Questions (12)

 54 $5^n+n$ is never prime? 43 Convergence of $\sqrt{n}x_{n}$ where $x_{n+1} = \sin(x_{n})$ 40 A zero sum subset of a sum-full set 36 Evaluating $\int P(\sin x, \cos x) \text{d}x$ 31 History of “Show that $44\dots 88 \dots 9$ is a perfect square”

### Tags (191)

 950 calculus × 141 464 integration × 43 737 real-analysis × 88 455 analysis × 52 725 sequences-and-series × 117 397 algebra-precalculus × 82 584 combinatorics × 121 393 trigonometry × 59 486 number-theory × 69 358 elementary-number-theory × 59

### Accounts (10)

 Mathematics 56,743 rep 4120211 Computer Science 3,810 rep 1438 Board & Card Games 3,492 rep 726 Theoretical Computer Science 1,470 rep 31527 Area 51 272 rep 3