A firm is manufacturing 2000 items. It is estimated that the rate of change of production $$P$$ with respect to additional number of workers $$x$$ is given by $$\frac{\mathrm{d} P}{\mathrm{~d} x}=100-12 \sqrt{x}$$. If the firm employs 25 more workers, then the new level of production of items is

$$\int \frac{3 x-2}{(x+1)(x-2)^2} \mathrm{~d} x=$$

(where $$C$$ is a constant of integration)

If the normal to the curve $$y=f(x)$$ at the point $$(3,4)$$ makes an angle $$\left(\frac{3 \pi}{4}\right)^c$$ with positive $$X$$-axis, then $$f^{\prime}(3)$$ is equal to

If $$P(A \cup B)=0.7, P(A \cap B)=0.2$$, then $$P\left(A^{\prime}\right)+P\left(B^{\prime}\right)$$ is