query: Express in gamma/beta functions $\int_{0}^{\pi/2}\tan^n x \ dx$
positive_passages.docid: 24056
positive_passages.text: Convergence of the improper integral $\int_{0}^{\pi/2}\tan^{p}(x) \; dx$
negative_passages.docid: 92176
negative_passages.text: Solving $\lim_{n\to\infty}(n\int_0^{\pi/4}(\tan x)^ndx)$?
negative_passages.docid: 106803
negative_passages.text: How to see $\cos x \leq \exp(-x^2/2)$ on $x \in [0,\pi/2]$?
negative_passages.docid: 54638
negative_passages.text: Integral $\int^{ \pi /2}_{0} \ln (\sin x)\ dx$
negative_passages.docid: 38773
negative_passages.text: Suppose $ \alpha, \beta>0 $. Compute: $ \int_{0}^{\infty}\frac{\cos (\alpha x)-\cos (\beta x)}{x}dx $
negative_passages.docid: 100907
negative_passages.text: $\sin\alpha + \sin\beta + \sin\gamma = 4\cos{\frac{\alpha}{2}}\cos{\frac{\beta}{2}}\cos{\frac{\gamma}{2}}$ when $\alpha + \beta + \gamma = \pi$
negative_passages.docid: 27347
negative_passages.text: Verify that $\left|\int_{\gamma} \exp(iz^2)dz\right| \leq \frac{\pi\big(1-\exp(-r^2)\big)}{4r}$ where $\gamma(t)=re^{it}$, for $0\leq t \leq \pi/4$.
negative_passages.docid: 126236
negative_passages.text: General closed form of $\int_{0}^{\theta_0} \frac{1}{\sqrt{\cos \theta-\cos \theta_0}} d\theta$
negative_passages.docid: 42279
negative_passages.text: Evaluating the indefinite integral $ \int \sqrt{\tan x} ~ \mathrm{d}{x}. $
negative_passages.docid: 73230
negative_passages.text: Roots of the incomplete gamma function
negative_passages.docid: 98787
negative_passages.text: Calculation of $\int \sqrt{\tan x+2}dx$
negative_passages.docid: 11499
negative_passages.text: How to show the inequality for $\int_{0}^{\pi/4}\tan^n(x) dx$
negative_passages.docid: 109316
negative_passages.text: How to calculate $\int_0^{\pi/2} \sin^a x \cos^b x \,\mathrm{d} x$
negative_passages.docid: 41028
negative_passages.text: Is there a combinatorial way to see the link between the beta and gamma functions?
negative_passages.docid: 158279
negative_passages.text: $\int_0^{\pi/2}\ln(\sin(x))$?
negative_passages.docid: 111601
negative_passages.text: Evaluating $\int \tan^{1/3}(\theta) d \theta$
negative_passages.docid: 3876
negative_passages.text: Did I derive a new form of the gamma function?