Evaluate \( \int_{6}^{10} \frac{5 x^{5}}{x^{3}-6} d x \)

\( \frac { \sqrt[ 3 ] { ( ( x _ { 0 } + \Delta x ) - 1 ) ^ { 2 } + \sqrt[ 3 ] { ( x _ { 0 } - 1 ) ^ { 2 } } } } { \Delta x \cdot ( \sqrt[ 3 ] { x _ { 0 } - 1 } + \sqrt[ 3 ] { x _ { 0 } - 1 } ) } \)

1. If \( y=3 t^{4}-\operatorname{tand} x=e^{-t^{2}} \), compute \( \left.\frac{d y}{d x}\right|_{t=0} \) 2. If \( y=3 t^{-2} \) and \( x=e^{-3 t} \), compute \( \left.\frac{d y}{d x}\right|_{t=0} \)

\( \int \int _ { s } f ( x , y , z ) d s = \int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 2 \pi } f ( s ( \phi , \theta ) ) \| \frac { \partial s } { \partial \phi } \times \frac { \partial s } { \partial \theta } \| d \theta d \phi \)

The enclosed area of the graph of the function \( Y=\left[x^{2}\right] \) and \( x \)-ares \( x=-2 \) to \( x=2 \) which is? \( 10-4(\sqrt{2}+\sqrt{2}) \) \( 10-5(\sqrt{5}+\sqrt{2}) \) \( 10-2(\sqrt{3}+\sqrt{2}) \) \( 10-8(\sqrt{2}+\sqrt{3}) \)

Розв'язати ДР з розподіленими змінними \( \mathrm{x}^{2} y^{\prime}=\frac{1}{\cos y} \).