Three vectors $\hat{\mathrm{i}}-\hat{\mathrm{k}}, \lambda \hat{\mathrm{i}}+\hat{\mathrm{j}}+(1-\lambda) \hat{\mathrm{k}}$ and $\mu \hat{\mathrm{i}}+\lambda \hat{\mathrm{j}}+(1+\lambda-\mu) \hat{\mathrm{k}}$ represents coterminous edges of a parallelopiped, then the volume of the parallelopiped depends on.

$$ \int \frac{\mathrm{d} x}{x\left(x^2+1\right)}= $$

The joint equation of the bisectors of the angles between the lines $x=5$ and $y=3$ is

If $\sin ^{-1} \frac{1}{3}+\sin ^{-1} \frac{3}{5}+\sin ^{-1} x=\frac{\pi}{2}$ then $x=$