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 38 Evaluate the integral: $\int_{0}^{1} \frac{\ln(x+1)}{x^2+1} \mathrm dx$ 22 Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$ 11 Visualizing Commutator of Two Vector Fields 11 infinite series involving harmonic numbers and zeta 11 Evaluate $\lim_{x \to \infty} \frac{1}{x} \int_x^{4x} \cos\left(\frac{1}{t}\right) \mbox {d}t$

### Reputation (2,364)

 +10 Evaluate the integral: $\int_{0}^{1} \frac{\ln(x+1)}{x^2+1} \mathrm dx$ +5 Sum equals integral +10 Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$ +10 Solving the integral $\int_{0}^{\infty} \frac{\sin{x}}{x} \ dx = \frac{\pi}{2}$?

### Questions (7)

 18 Sum equals integral 4 Inequality between volume and its projections 3 Integration in n-spherical coordinates 3 Improper integral and special functions 2 Divergence in spherical coordinates

### Tags (30)

 114 calculus × 16 46 sequences-and-series × 7 79 real-analysis × 7 34 complex-analysis × 5 76 integration × 13 24 improper-integrals × 5 54 definite-integrals × 5 17 analysis × 4 50 limits × 5 11 inequality × 5

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