TheOscillator
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 18 Definite integral - closed form: $\int_{0}^{\infty}\cos\left(x^{4} + 1 \over x^{2}\right)\,{\rm d}x$ 8 Trigonometric Integrals $\int \frac{1}{1+\sin^2(x)}\mathrm{d}x$ and $\int \frac{1-\tan(x)}{1+\tan(x)} \mathrm{d}x$ 8 How to prove $\lim_{n \to \infty} e^n \cdot \left( \sum_{k=0}^{n-1} ({k-n \over e})^k/k! \right)- 2 \cdot n = \frac 23$? 8 How to find the integral $\displaystyle\int_{0}^{\infty}\frac{\arctan{x}}{2+x^2}dx$ 5 Evaluating $\sum\frac{1}{1+n^2+n^4}$

Reputation (1,751)

 +30 If $H$ is a subgroup of $G$ of index $n$, then $g^{n!} \in H \ \forall g \in G$ +10 Prove series converge for almost every $x$ +10 How to find the integral $\displaystyle\int_{0}^{\infty}\frac{\arctan{x}}{2+x^2}dx$ +10 Trigonometric Integrals $\int \frac{1}{1+\sin^2(x)}\mathrm{d}x$ and $\int \frac{1-\tan(x)}{1+\tan(x)} \mathrm{d}x$

Questions (8)

 5 Ideal in a ring of continuous functions 4 $\mathcal{L}^2$-norm of the Laplace transform 2 Closure of a pre compact subspace is compact? 2 Evaluating a sum $-\zeta'(2)$ 2 Complex Integral with exponential

Tags (57)

 70 integration × 20 18 real-analysis × 15 46 calculus × 14 18 closed-form × 2 36 definite-integrals × 9 17 limits × 7 27 improper-integrals × 6 8 trigonometry × 2 22 sequences-and-series × 8 8 exponential-function

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 Mathematics 1,751 rep 1515 Cross Validated 101 rep 2 MathOverflow 101 rep 2