Integration with Fractional Part (Calculus) $\lim\limits_{n\to \infty} \int\limits_0^1{e^{\{nx\}}\cdot x^{2016}dx} $
51884
Compute: $\lim\limits_{n\to+\infty}\int\limits_{0}^1 e^{\{nx\}}x^{100}dx$
8289
Hints on calculating the integral $\int_0^1\frac{x^{19}-1}{\ln x}\,dx$
56394
What should be the limits in this integration
15625
Computing $\int_0^\infty\mathrm{d} x\frac{x}{e^x+1}$ with contour integration
65015
Computing $\lim_{n \to \infty} \sqrt[n]{ \int_{0}^{1} (1+x^n)^n dx}$
33675
Find $\lim_{n\to \infty} \int_n^{n+1} {\sin x \over x} dx$
36648
The limit of $((1+x)^{1/x} - e+ ex/2)/x^2$ as $x\to 0$
155206
Convergence in probability: $\lim_{n\to\infty}\int_0^1\cdots\int_0^1\frac{x_1^2+x_2^2+\cdots+x_n^2}{x_1+x_2+\cdots +x_n}dx_1\cdots dx_n=\frac23$
154605
How to compute $\lim\limits_{n\rightarrow \infty} \{(2+\sqrt{3})^{n}\}$, where $\{x\}$ is the fractional part of $x$?
109059
Evaluate $\lim\limits_{n\to \infty}\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{6n}$
151149
$\lim_{n \to \infty} n \int_{1}^{\infty} \frac{dx}{1+x^n}$, solution critique needed
76990
Find $\lim_{x \to - \infty} \left(\frac{4^{x+2}- 2\cdot3^{-x}}{4^{-x}+2\cdot3^{x+1}}\right)$
1392
$\int_{0}^{\infty}{\left(x^3\cdot(e^x-1)^{-1} \right)}dx$
113289
finding the limit $\lim\limits_{x \to \infty }(\frac{1}{e}(1+\frac{1}{x})^x)^x$
144273
Find $\lim_{n\to\infty} \frac{1}{n} \int_0^\infty f(x) e^{-a_n x} dx$
53518
Integrating : $\int_0^1 {\frac {x^a-x^b} {\ln x} dx}$
65982
Evaluate the improper integral $ \int_0^1 \frac{\ln(1+x)}{x}\,dx $