How to prove that: $\int_\Bbb R f(x)dx = \int_\Bbb R f(x-\frac{1}{x})dx$
8829
How to prove $\int_{-\infty}^{+\infty} f(x)dx = \int_{-\infty}^{+\infty} f\left(x - \frac{1}{x}\right)dx?$
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
66145
>Prove that $\frac d {dx} x^n=nx^{n-1}$ for all $n \in \mathbb R$.
61782
How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
139453
Prove that $\frac{1}{f'(a)} = \frac{1}{2\pi i} \int_C \frac{1}{f(z)-f(a)} dz$
62524
Showing that $\int\limits_{-a}^a \frac{f(x)}{1+e^{x}} \mathrm dx = \int\limits_0^a f(x) \mathrm dx$, when $f$ is even
1641
Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
88154
Proving $\int_{0}^1\frac{x-1}{\log x}dx=\log 2$ and $\int_{0}^1\frac{\log x}{x-1}dx=\frac{\pi^2}{6}$
114734
Prove that $\frac{1}{2\pi i}\int_\mathcal{C} |1+z+z^2+\cdots+z^{2n}|^2~dz =2n$ where $\mathcal{C}$ is the unit circle
93806
$\|f\|_{L^{p}}=\sup\left\{\int_{{\bf R}^{n}}|f(x)g(x)|~dx:\|g\|_{L^{q}}\le1\right\}$
46310
Showing that $ \int_{0}^{1} \frac{x-1}{\ln(x)} \mathrm dx=\ln2 $
64571
Prove that $\int_{E}f =\lim \int_{E}f_{n}$
7903
Prove that $B[x] \cap B[x^{-1}]$ is integral over $B$
62192
Proof $L{\rm{[}}\frac{{x(t)}}{t}{\rm{] = }}\int_s^\infty {X(u)du} $
73489
How is the Integral of $\int_a^bf(x)~dx=\int_a^bf(a+b-x)~dx$
105707
A proof of $\int_{0}^{1}\left( \frac{\ln t}{1-t}\right)^2\,\mathrm{d}t=\frac{\pi^2}{3}$
105527
Show that $\lim_{r\to 0} \frac{1}{r^2}\int_{C_{r}}f(z)dz = 2 \pi i\frac{\partial f}{\partial \bar{z}}(z_0)$