If $\quad \int \frac{3 \sin x \cos x}{4 \sin x+7} \mathrm{~d} x=\mathrm{A} \sin x-\mathrm{Blog}(4 \sin x+7)+\mathrm{c}$ where c is the constant of integration, then the value of $\mathrm{A}+\mathrm{B}$ is equal to

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