How to integrate this type of integral: $\lim_{n \rightarrow \infty}{\int_ 0^1}\frac{n x^{n-1}}{1+x}dx$
11489
Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$
27156
Sequence Limit: $\lim\limits_{n \rightarrow \infty}{n\,x^n}$
90095
Integrate $\int_0^{\infty } \frac{\cos x}{x} dx$
147977
Evaluate $\int_0^1\left(\frac{x-1}{x+1}\right)^n\frac{1}{\ln x} \,dx$
140574
Find $\lim_{n\to \infty} \int_0^1 nx^n e^{x^2} dx$
151149
$\lim_{n \to \infty} n \int_{1}^{\infty} \frac{dx}{1+x^n}$, solution critique needed
145233
How to show $\lim_{n \rightarrow \infty} \int_0^1 n x^n f(x) \; dx = f(1)$ for continuous $f$?
44054
Evaluating the integral $\mathop{\lim}\limits_{n \to \infty} \int_{-1}^{1} f(t)\cos^{2}(nt) \ dt $
119145
$\lim\limits_{n\rightarrow\infty} \sqrt{n}(\sqrt{n+1}-\sqrt{n})$
146349
$\int_0^\infty \frac{\ln\left(1+x-\sqrt{2x}\right)}{1+x^2}\,dx$
45806
Finding $\lim\limits_{n \rightarrow \infty}\left(\int_0^1(f(x))^n\,\mathrm dx\right)^\frac{1}{n}$ for continuous $f:[0,1]\to[0,\infty)$
104691
Integration of $\int_{0}^{1} \frac{x^k}{1-x} dx$
5521
Evalute $ \lim_{n\rightarrow \infty}\sum^{n}_{k=0}\frac{\binom{n}{k}}{n^k(k+3)} $
110588
Showing $\lim_{n\rightarrow\infty}\sqrt[3]{n^3+n^2}-\sqrt[3]{n^3+1}\rightarrow\frac{1}{3}$
156546
Evaluate the limit $\lim_{n\rightarrow \infty}\frac{1}{\sqrt{n}}\left(1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\ldots+\frac{1}{\sqrt{n}}\right)$
139784
Computing integration $\int_0^1\frac{\ln x}{1-x}d x$
95991
How to solve $\lim_{x \rightarrow 0} {\frac{(1+x)^a-1}{x}}$?