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### Questions (104)

 18 Integrating $\int_0^\infty\frac{\log (1+z^2)}{e^z-1}dz$ using residue calculus. 12 Can a substitution cause a convergent definite integral to diverge? 11 proof that $e^x$ is a transcendental function of $x$? 11 Integration method for $\int_0^\infty\frac{x}{(e^x-1)(x^2+(2\pi)^2)^2}dx=\frac{1}{96} - \frac{3}{32\pi^2}.$ 8 Is it possible to express $e$ in terms of $\pi$ algebraically and vice-versa?

### Reputation (2,592)

 +5 Are Taylor series and power series the same “thing”? +5 Why is the kernel of an isomorphism always equal to the identity? +5 Solving $z=w/2-\sin(tw)/(2t)$ for $w$ +10 $(\delta,\varepsilon)$ Proof of Limit

 11 Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \ \mathrm dx$ 10 Why does being holomorphic imply so much about a function? 8 Two methods to integrate? 4 What is the closed form for $S=\displaystyle\sum_{n=1}^{\infty} \dfrac{\sin ({n})}{n!}$? 4 Calculating $x= \sqrt{4+\sqrt{4-\sqrt{ 4+\dots}}}$

### Tags (113)

 29 calculus × 18 6 definite-integrals × 20 18 complex-analysis × 30 6 trigonometry × 5 13 integration × 18 5 summation × 2 10 soft-question × 9 4 sequences-and-series × 7 9 algebra-precalculus × 7 4 notation × 7

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