Evaluate $P.V. \int^{\infty}_{0} \frac{x^\alpha }{x(x+1)} dx $ where $0 < \alpha <1$
5537
Closed form for $ \int_0^\infty {\frac{{{x^n}}}{{1 + {x^m}}}dx }$
6014
Evaluating $\int_{-\infty}^{\infty}\frac{\exp\left(-a x^2\right)}{x^2+b^2}dx$
58646
Are there any ways to evaluate $\int^\infty_0\frac{\sin x}{x}dx$ without using double integral?
74955
Simplify result of $\int_0^{\infty} \frac{1}{1+x^n}dx$
130935
Evaluating $\int_{0}^{1}\frac{x-1}{(x+1)\ln x} dx $
98365
How to evaluate $\lim_{x \rightarrow \infty} \left(\left(\frac{x+1}{x-1}\right)^x -e^2\right){x}^2$
38773
Suppose $ \alpha, \beta>0 $. Compute: $ \int_{0}^{\infty}\frac{\cos (\alpha x)-\cos (\beta x)}{x}dx $
50471
Evaluate $\int\frac1{1+x^n}dx$ for $n\in\mathbb R$
100194
Calculating $ \int _{0} ^{\infty} \frac{x^{3}}{e^{x}-1}\;dx$
147977
Evaluate $\int_0^1\left(\frac{x-1}{x+1}\right)^n\frac{1}{\ln x} \,dx$
27195
Evaluating $\int_{0}^{1}\frac{1-x}{1+x}\frac{\mathrm dx}{\ln x}$
7042
Defined integral of $x^{\alpha} (1-x)^{\beta-1}$
100180
Evaluate the integral $\int_0^\infty \frac{dx}{\sqrt{(x^3+a^3)(x^3+b^3)}}$
105860
Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$
137549
Given $\int_0^{\infty}e^{-x^2}dx = \frac{\sqrt{\pi}}{2}$, evaluate $\int_0^{\infty}e^{-a^2x^2-\frac{b^2}{x^2}}dx $
58909
Evaluation of $\int\frac{dx}{x+ \sqrt{x^2-x+1}}$
20956
Correct way to prove the limit: $\mathop {\lim }\limits_{x \to 0} {x^\alpha }\int\limits_x^1 {\frac{{f\left( t \right)}}{{{t^{\alpha  + 1}}}}dt} $?