Daily Math · 2026-05-24

Question 1

Calculați $\log_4 8$.

Accepted Answer

$\dfrac{3}{2}$

Answer

$\dfrac{1}{2}$

Answer

$\dfrac{2}{3}$

Answer

$2$

Question 2

Find $\displaystyle\int\dfrac{1}{x^2-1}\,dx$.

Accepted Answer

$\dfrac{1}{2}\ln\!\left|\dfrac{x-1}{x+1}\right| + C$

Answer

$\ln\!\left|\dfrac{x-1}{x+1}\right| + C$

Answer

$\arctan x + C$

Answer

$\ln|x^2-1| + C$

Answer

$\dfrac{1}{2}\ln|x^2-1| + C$

Answer

$\dfrac{1}{2}\ln\!\left|\dfrac{x+1}{x-1}\right| + C$

Question 3

By the rational-root theorem, possible rational roots of $P(X) = 2X^3 + 3X^2 - 1$ are of the form $\dfrac{p}{q}$ with $p \mid 1$ and $q \mid 2$. They are:

Accepted Answer

$\pm 1, \pm \dfrac{1}{2}$

Answer

$\pm 1, \pm 2$

Answer

$\pm 1, \pm 3, \pm 2$

Answer

$\pm 1$ only