qoqosz

 63 Evaluate the integral: $\int_{0}^{1} \frac{\ln(x+1)}{x^2+1} \mathrm dx$ 27 Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$ 15 Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$? 14 Visualizing Commutator of Two Vector Fields 14 Norm of integral operator in $L_2$

### Reputation (3,192)

 +10 Norm of integral operator in $L_2$ +30 Evaluate the integral: $\int_{0}^{1} \frac{\ln(x+1)}{x^2+1} \mathrm dx$ +10 “Sum equals integral” identities similar to $\int_0^1 \frac{dx}{x^x} = \sum_{n = 1}^{\infty} \frac{1}{n^n}$ +10 Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$?

### Questions (8)

 22 “Sum equals integral” identities similar to $\int_0^1 \frac{dx}{x^x} = \sum_{n = 1}^{\infty} \frac{1}{n^n}$ 4 Improper Integral from Gradshteyn and Ryzhik [duplicate] 4 Inequality between volume and its projections 3 Find the special function form of $\int_0^{+\infty} \left(\sqrt{1+x^4} - x^2\right) dx$ 3 Divergence in spherical coordinates

### Tags (30)

 157 calculus × 16 53 sequences-and-series × 7 110 real-analysis × 7 47 complex-analysis × 5 102 integration × 14 37 improper-integrals × 6 92 definite-integrals × 5 30 analysis × 4 56 limits × 5 15 differential-geometry × 2

### Bookmarks (22)

 439 Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$ 266 Funny identities [closed] 236 Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$? 193 Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \frac{\sqrt \pi}{2}$ 85 Conjecture $\int_0^1\frac{\mathrm dx}{\sqrt{1-x}\ \sqrt[4]x\ \sqrt[4]{2-x\,\sqrt3}}\stackrel?=\frac{2\,\sqrt2}{3\,\sqrt[8]3}\pi$