### Answers (298)

 30 Number which is simultaneously sum of 2 and 3 squares 22 Derivative of a function w.r.t. another function. 13 Zeroes of a non elementary integral 13 What does .9 with a line above the 9 mean? 11 How to solve $x^x=100$?

### Reputation (8,449)

 +10 Solving an exponential equation involving e: $e^x-e^{-x}=\frac{3}{2}$ +10 What's the value of tau? +10 Integral $\int_0^\infty \frac{\arctan(x) dx}{x(1+x^2)}$? +10 How to prove $\int_0^1 \frac{\arctan( a x)}{x \sqrt{1 - x^2}} dx = \frac{\pi}{2} \ln (a + \sqrt{1 + a^2})$?

### Questions (59)

 16 How to evaluate $\sum\limits_{k=0}^{n-1} \sin^t(\pi k/2n)$? 13 Prove that $\lim_{n\rightarrow \infty} \frac{\log_{10}\lfloor\text{Denominator of } H_{10^n}\rfloor+1 }{10^n}=\log_{10} e$ 12 Prove $\int_{-\pi}^{\pi}\sin \sin x \,dx=0$ without using the fact that $\sin(x)$ is odd. 11 Limit of recursive sequence with floor 10 Show that $\int_0^1 \prod_{n\geq 1} (1-x^n) \, dx = \frac{4\pi\sqrt{3}\sinh(\frac{\pi}{3}\sqrt{23})}{\sqrt{23}\cosh(\frac{\pi}{2}\sqrt{23})}$ [duplicate]

### Tags (161)

 121 calculus × 80 43 derivatives × 14 85 algebra-precalculus × 55 38 sequences-and-series × 37 70 integration × 41 37 complex-numbers × 20 49 trigonometry × 31 36 number-theory × 9 45 definite-integrals × 19 28 limits × 34

### Bookmarks (114)

 265 How does one prove the determinant inequality $\det\left(6(A^3+B^3+C^3)+I_{n}\right)\ge 5^n\det(A^2+B^2+C^2)$? 57 Is there a “good” reason why $\left\lfloor \frac{n!}{11e}\right\rfloor$ is always even? 50 Infinite Integration by Parts 49 Proof (claimed) for Riemann hypothesis on ArXiv [closed] 48 Evaluate $\int_{0}^{\pi/2}\frac{1+\tanh x}{1+\tan x}dx$

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