show that $\int_0^1 (\sqrt[3]{1-x^7}-\sqrt[7]{1-x^3}) \, dx=0$
100869
How to show that $\int_0^1 \left(\sqrt[3]{1-x^7} - \sqrt[7]{1-x^3}\right)\;dx = 0$
23071
Showing that $f_0 (x_1, \ldots, x_m) \mathrm tr A =\displaystyle{ \sum_{i=1}^n} f_0(x_1, \ldots, Ax_i,\ldots, x_m)$
103598
Showing that $\int_0^1 \log(\sin \pi x)dx=-\log2$
122407
If $f(x) = x^3+3x+4\;,$ Then value of $ \int_{-1}^{1}f(x)dx+\int_{0}^{4}f^{-1}(x)dx$
9730
Solve the integral $\int_0^\infty x/(x^3+1) dx$
33389
What's the minimum of $\int_0^1 f(x)^2 \: dx$, subject to $\int_0^1 f(x) \: dx = 0, \int_0^1 x f(x) \: dx = 1$?
157847
If $x_n \to 0$, show that $\sqrt{x_n} \to 0$
61162
Show that $\left(\int_0^1 f(x)\,dx\right)^2\leq2\int_0^1x\, f(x)^2\,dx $
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
110826
prove that : $ i = \sqrt {-1}\ $
57659
Evaluate $\int_{\left | z \right |=3} (e^{z}-1)dz/(z(z-1)(z-i))$
133851
How to arrive at $\int_{0}^{1} f^3(x) \, dx < (\int_{0}^{1} f(x) \, dx)^2$?
17996
Integral $\int_0^1 \frac{\ln(x+\sqrt{1-x^2})}{x}dx$
131120
Proving an integral equation.
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
98836
Showing $\int_x^{x+1}f(t)\,dt \xrightarrow{x\to\infty}0$ for $f\in L^2 (\mathbb{R})$
117246
Show that $\lim\limits_{a \to 0^+} \int^1_0 ax^{a−1}f(x)dx=f(0)$.