If $$I=\int \frac{e^x}{e^{4 x}+e^{2 x}+1} d x$$ and $$J=\int \frac{e^{-x}}{e^{-4 x}+e^{-2 x}+1} d x$$, then for any arbitrary constant $$C$$, than the value of $$J-I$$ equals

The principal value of $$\sin ^{-1}(\sin (3 \pi / 4))$$ is

If $$x=\log _e\left(\frac{\cos \frac{y}{2}-\sin \frac{y}{2}}{\cos \frac{y}{2}+\sin \frac{y}{2}}\right), \tan \frac{y}{2}=\sqrt{\frac{1-t}{1+t}}$$ Then, $$\left(y_1\right)_{t=1 / 2}$$ has the value

The c.d.f. $$F(x)$$ associated with p.d.f. $$f(x)$$

$$f(x)=\left\{\begin{array}{cl}12 x^2(1-x), & \text { if } 0< x <1 \\ 0 ; & \text { otherwise }\end{array}\right.$$ is