Number of real solutions of the equation $1+8^x+27^x = 2^x+12^x+9^x$

$f \in L^1$, but $f \not\in L^p$ for all $p > 1$

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Solve $\lfloor \sqrt x \rfloor = \lfloor x/2 \rfloor$ for real $x$

Calculation of $\int_0^{\pi} \frac{\sin^2 x}{a^2+b^2-2ab \cos x}\mathrm dx$

Evaluation of $\prod_{n=1}^\infty e\left(\frac{n}{n+1}\right)^{n}\sqrt{\frac{n}{n+1}}$

Integration $\frac{1}{2\pi}\int_{-\pi}^{\pi}(x-a)^ke^{-i\omega x}dx, \ \ \ \ a\in\mathbb R$.

Proof that an involutory matrix has eigenvalues 1,-1

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Suppose that $f ' (x)$ exists and $f(x)$ has two roots $x_1$ and $x_2$. Try to prove that:

Convergence of the integral of $\frac{\cos(x)}{x^2}$

Interesting Question on Ants

Are determinants always real?

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