Real analytic methods for the following integral
28771
Prove that $\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx =\frac{\pi e}{24} $
101174
A closed form for a triple integral with sines and cosines
98678
Finding the following definite and indefinite integrals
23087
Evaluate $\int_0^\infty \frac{(\log x)^2}{1+x^2} dx$ using complex analysis
126046
solving the integral $ \int_0^\infty \dfrac{\sin xt}{x(x^2+1)} dx $
115469
Integral of Sinc Function Squared Over The Real Line
52864
Line integration in complex analysis
102636
Contour Integral: $\int^{\infty}_{0}(1+z^n)^{-1}dz$
59532
Evaluation of this integral.
151649
Exact Values of the integal $\int_0^\infty \frac{r^{n-1}}{(1+r^2)^{\frac{s}{2}}}\,dr$
25509
evaluation of an integral involving algebraic numbers
136981
How can I solve this integral using the Residue theorem?
125523
How to find $\int_{0}^{\pi/2} \log ({1+\cos x}) dx$ using real-variable methods?
123694
How to compute the integral $\int_{0}^{\infty} \frac{x^{1/3}}{1+x^{2}} \ dx$
30193
Real-Analysis Methods to Evaluate $\int_0^\infty \frac{x^a}{1+x^2}\,dx$, $|a|<1$.
148914
Total Variation and indefinite integrals
91196
Complex Integration of $\int_0^\infty e^{-ax}\cos(bx)\,dx$