29 Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$ 20 Express 99 2/3% as a fraction? No calculator 15 How to remember trig identities? 13 Cross product in higher dimensions 11 Why does being holomorphic imply so much about a function?

### Reputation (8,766)

 +10 Are Taylor series and power series the same “thing”? +10 “Length” function without absolute homogeneity property? +10 How to denote matrix concatenation? +10 Name for “3D quadrilateral” shape?

### Questions (164)

 22 Are Taylor series and power series the same “thing”? 19 Multiplying two inequalities 19 Integrating $\int_0^\infty\frac{\log (1+z^2)}{e^z-1}dz$ using residue calculus. 13 Proof that $e^x$ is a transcendental function of $x$? 12 Can a substitution cause a convergent definite integral to diverge?

### Tags (204)

 91 calculus × 32 41 closed-form × 5 49 integration × 34 34 contour-integration × 10 47 definite-integrals × 26 28 trigonometry × 12 42 complex-analysis × 55 26 real-analysis × 30 42 algebra-precalculus × 21 26 linear-algebra × 13

### Bookmarks (297)

 1052 Is $\frac{\textrm{d}y}{\textrm{d}x}$ not a ratio? 925 Can I use my powers for good? [closed] 716 Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ (Basel problem) 570 Why is $1 - \frac{1}{1 - \frac{1}{1 - \ldots}}$ not real? 438 Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$