\( \int _{}^{}3\sqrt {x}+(\frac{10}{x^{6}}) d \)

El volumen del sólido limitado superiormente por \( z=x^{2}+y^{2} \) e inferiormente por la región \( R=\{(x, y),|x| \leq 1,|y| \leqslant 1\} \) es: (A) \( \frac{8}{3} u^{3} \) (B) \( \frac{7}{3} u^{3} \) (C) \( \frac{5}{3} u^{3} \) (D) \( \frac{4}{3} u^{3} \)

Find the derivative of the given function. \( f(x)=\tanh ^{-1}(4 x) \) \( f^{\prime}(x)=\square \)

During the time interval \( 4 \leq t \leq 16 \), the total number of wolves in a forest can be modeled by the function \( V(t)=-133 \cos \left(0.03 t^{2}\right)+211 \), where \( t \) is measured in weeks. What is the average rate of change in the number of wolves in the forest from time \( t=4 \) to time \( t=16 ? \) You may use a calculator and round to the nearest thousandth. Indicate units of measure.

El volumen del sólido limitado superiormente por el paraboloide \( z=2-x^{2}-y^{2} \) e inferiormente por el plano \( 2 z=1 \) es: (A) \( \frac{9}{8} \pi u^{3} \) (B) \( \frac{7}{8} \pi u^{3} \) (C) \( \frac{5}{8} \pi u^{3} \) D) \( \frac{3}{8} \pi u^{3} \)

Find the integral by the simplest method. \( \int 6 x \cos (2 x) d x=\square \)