24 “What if” math joke: the derivative of $\ln(x)^e$ 12 Evaluating $\int_{0}^{\infty} \left[\left(\frac{2015}{2015+x}+\cdots +\frac{2}{2+x}+\frac{1}{1+x}-x\right)^{2016}+1 \right] ^{-1}\mathrm{d}x$ 11 Can someone explain these strange properties of $10, 11, 12$ and $13$? 9 Denesting radicals like $\sqrt{\sqrt{2} - 1}$ 8 Books Preparatory for Putnam Exam

### Reputation (4,885)

 +10 Evaluating a definite integral: $\int_0^{\pi}\frac{x}{1-\sin{x}\cos{x}}\,\mathrm dx$ +10 Suggestions for a good statistics book and a calculus book? +10 What is the derivative of: $f(x)=x^{2x^{3x^{4x^{5x^{6x^{7x^{.{^{.^{.}}}}}}}}}}$? +10 Evaluate $\int [\cos(\csc^{-1}(\tan(\sec^{-1} (\cot(\sin^{-1}(\sec(\cot^{-1}(\csc(\cos^{-1}(x))))))))))]^2 dx$

### Questions (72)

 35 What is the derivative of: $f(x)=x^{2x^{3x^{4x^{5x^{6x^{7x^{.{^{.^{.}}}}}}}}}}$? 23 Analytic form of: $\int \frac{\bigl[\cos^{-1}(x)\sqrt{1-x^2}\bigr]^{-1}}{\ln\bigl( 1+\sin(2x\sqrt{1-x^2})/\pi\bigr)} dx$ 14 How can I evaluate the following integral? $\int(\sqrt{x}-x)(e^{\arctan\sqrt{x}})^2dx$ 11 Doubt regarding divisibility of the expression: $1^{101}+2^{101} \cdot \cdot \cdot +2016^{101}$ 10 What is the derivative of $x!^{x!^{x!^{x!^{x!^{x!^{x!^{.{^{.^{.}}}}}}}}}}$

### Tags (119)

 56 calculus × 49 24 popular-math 31 logarithms × 11 23 integration × 37 27 derivatives × 11 22 algebra-precalculus × 9 25 recreational-mathematics × 4 22 soft-question × 6 24 exponential-function × 2 21 book-recommendation × 6

### Bookmarks (129)

 1363 Visually stunning math concepts which are easy to explain 548 Examples of patterns that eventually fail 467 Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$ 466 “The Egg:” Bizarre behavior of the roots of a family of polynomials. 335 'Obvious' theorems that are actually false