Find the indefinite integral. \( \int \frac{1}{2+5 x^{6}}\left(30 x^{5}\right) d x \) \( \int \frac{1}{2+5 x^{6}}\left(30 x^{5}\right) \cdot d x=\square \)

\( ( x ) = \frac { x } { 3 } - \frac { 3 } { x } ; \quad f ^ { \prime } ( 3 ) = ? \)

\begin{tabular}{l} Question \\ Given \( F(x) \) below, find \( F^{\prime}(x) \). \( F(x)=\int_{x}^{5} \sqrt{2 t-2} d t \) \\ Provide your answer below: \\ \hline\( F^{\prime}(x)=\square \)\end{tabular}

A company manufactures and sells \( x \) clocks per week with weekly price-demand function: \( f(p)=30-3 p \) where \( p \) is the price per clock. a. Compute the elasticity of demand function, \( E(p) \), for this demand function. \( E(p)= \) b. At \( p=3 \), a price increase of \( 2 \% \) will create a demand decrease of what percent? Round to 2 decimal places if necessary.

Find \( \frac{\mathrm{dy}}{\mathrm{dx}} \) for function, \( y=\frac{3 x^{2}}{\sqrt{2 x^{2}+3}} \)

Question Given \( f(x) \) below, find \( f^{\prime}(x) \) \[ f(x)=\int_{\sqrt{x}}^{x^{3}} t^{4} d t \]