Can contour integration be used to integrate $~u^u(1-u)^{1-u}~$?
28771
Prove that $\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx =\frac{\pi e}{24} $
29304
Surface integral of a scalar over a unit cube.
98710
Finding $\int_0^{\infty}xe^{-\lambda x} \, dx$
124401
How to evaluate $\int_0^{2\pi}\frac{1}{(1+a\cos {\theta})^2}\,d\theta$ without contour integration?
86857
Integrate $\int_{0}^{2\pi}\log|1-e^{i\theta}| d\theta$
129947
Integral of $\log(\sin(x))$ using contour integrals
121988
Asymptotic expansion of the complete elliptic integral of the first kind
108284
Integration and existence of an antiderivative
99113
Reverse Cauchy Schwarz for integrals
85736
Evaluating the integral $\int_{-1}^{1} \frac{\sqrt{1-x^{2}}}{1+x^{2}} \, dx$ using a dumbbell-shaped contour
91196
Complex Integration of $\int_0^\infty e^{-ax}\cos(bx)\,dx$
84311
Elliptic integral $\int^1_0 \frac{K(k)}{\sqrt{1-k^2}}\,dk$
45682
Show that there exists a unique $v_0 \in H^1(0,1)$ such that $u(0)=\int_0^1(u'v_0'+uv_0), \forall u \in H^1(0,1)$
42789
Integrate by Partial Fractions or Substitution
7042
Defined integral of $x^{\alpha} (1-x)^{\beta-1}$
101045
Is there a closed form for the integral $\int_0^1 x^n \log^m (1-x) \, {\rm d}x$?
85618
Integral of $\frac{x^\alpha}{(1 + x^2)^2}$ from 0 to $\infty$ using contour integration for $-1 < \alpha <3$