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.).

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.

\( \lim _ { n \rightarrow \infty } [ \frac { 1 } { \sqrt { 4 n ^ { 2 } - 1 } } + \frac { 1 } { \sqrt { 4 n ^ { 2 } - 2 ^ { 2 } } } + \cdots + \frac { 1 } { \sqrt { 3 n ^ { 2 } } } ] \)

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

(d) \( \lim _{n \rightarrow+\infty} \frac{\operatorname{sen}(1 / n)}{\operatorname{sen}(3 / n)} \)

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