(5) \( \int x^{n} d x= \)

\( \int _{0}^{1}\frac{1-\cos (x)}{\sqrt {x^{5}}+5x^{3}} d x \)

Evaluate the triple integral. \[ \iiint_{G} x y \sin (y z) d V \] where \( G \) is the rectangular box defined by the inequalities \( 0 \leq x \leq \pi, 0 \leq y \leq 17,0 \leq z \leq \frac{\pi}{102} \)

Find the volume of the solid formed by rotating the area under the curve \( y = \frac{1}{x} \) from \( x = 1 \) to \( x = 3 \) about the y-axis.

18. \( \int_{-2}^{-1} 4 x^{3} d x \) 19. \( \int_{-1}^{0} 3 x^{2} d x \)

Evaluate the triple integral. \[ \iiint_{G} x y z d V \] where \( G \) is the solid in the first octant that is bounded by the parabolic cylinder \( z=3-x^{2} \) and the planes \( z=0, y=x \) and \( y=0 \).