How to evaluate $ \int_0^n \cos(2\pi \lfloor x\rfloor\{x\})dx$?
47923
For $n\in\mathbb{N}$, evaluate $\int_0^n \cos(2\pi \lfloor x\rfloor\{x\})dx$
96791
How to show that $\lfloor n/1\rfloor+\lfloor n/2 \rfloor+....+\lfloor n/n\rfloor+\lfloor{\sqrt{n}}\rfloor$ is even?
72039
Compute $\int_0^\infty\frac{\cos(xt)}{1+t^2}dt$
18841
Ways to evaluate $\int \sec \theta \, \mathrm d \theta$
96414
Using residues to evaluate the integral $\int_{-\pi}^{\pi} \frac{\cos(n\theta)}{1-2a\cos(\theta)+a^2}d\theta$, $|a|<1$
65847
To evaluate $\int_{0}^\pi \frac {\sin^2 x}{a^2-2ab \cos x + b^2}\mathrm dx$?
31964
Evaluating $\int_0^{\infty}\frac{\ln(x^2+1)}{x^2+1}dx$
76828
Evaluating $\sum_{i = 0}^{\lfloor n/2 \rfloor} {n \choose 2i}p^{2i}(1 - p)^{n - 2i}$
74822
How to evaluate $\int_{0}^{\pi }\theta \ln\tan\frac{\theta }{2} \, \mathrm{d}\theta$
45480
Does $\sum\frac{(-1)^{\lfloor \sqrt n\rfloor}}{ n}$ converge?
135519
How to approach solving $\int_0^{\pi/2} \ln(a^2 \cos^2 x +b^2 \sin^2 x ) dx$
60491
Evaluate $ \int_{25\pi/4}^{53\pi/4}\frac{1}{(1+2^{\sin x})(1+2^{\cos x})}dx $
147977
Evaluate $\int_0^1\left(\frac{x-1}{x+1}\right)^n\frac{1}{\ln x} \,dx$
12604
Evaluate $\int_0^\pi xf(\sin x)dx$
158279
$\int_0^{\pi/2}\ln(\sin(x))$?
95933
How to evaluate the integral $\int_0^{\pi}\frac{a^n\sin^2x+b^n\cos^2x}{a^{2n}\sin^2x+b^{2n}\cos^2x}dx$?
46736
Limits involving trigonometric functions $f(x)=\lfloor{x^2 \rfloor} \sin^2(\pi x)$