Evaluate the integral. \( \int_{3}^{3}\left(x^{2}-8 x+6\right)^{8} d x \) \( \int_{3}^{3}\left(x^{2}-8 x+6\right)^{8} d x=\square \) (Type an exact answer in simplified form.).

2. \( \left\{x_{n}\right\} \) ketma-ketlikning yuqori va quyi limitlari topilsin. \( x_{n}=\left(1+\frac{1}{n}\right)^{n}(-1)^{n}+\sin \frac{n \pi}{4} \) 3. Limit hisoblansin. \( \lim \left(\sqrt{1+x+x^{2}}-\sqrt{1-x+x^{2}}\right) \)

Solve the differential equation \( \frac{dy}{dx} = 6y \) using separation of variables.

\( \int _ { - \infty } ^ { \infty } x ^ { 4 } e ^ { - x ^ { 3 } } d x \)

Find differenthal equation of the primitue \( x y+x^{2} y+y^{2}=13 \)

Given that \( \int_{0}^{1}\left(2+3 \cos \frac{1}{2} x\right) d x=\int_{-1}^{2} e^{2 x+1} d x \), find the value of \( k \), giving your answer correct to 3 decimal places.