Identify u and $d u / d x$ for the integral $\int \left( 8 + \frac { 1 } { x ^ { 8 } } \right) ^ { 8 } \left( - \frac { 8 } { x ^ { 9 } } \right) d x$ .
A) $u = 8 + \frac { 1 } { x ^ { 8 } }$ and $d u / d x = \frac { 8 } { x ^ { 9 } }$
B) $u = \left( 8 + \frac { 1 } { x ^ { 8 } } \right) ^ { 7 }$ and $du / d x = - \frac { 8 } { x ^ { 9 } }$
C) $u = 8 + \frac { 1 } { x ^ { 8 } }$ and $d u/ d x = - \frac { 8 } { x ^ { 9 } }$
D) $u = 8 + \frac { 1 } { x ^ { 8 } }$ and $d u / d x = - \frac { 9 } { x ^ { 9 } }$
E) $u = \left( 8 + \frac { 1 } { x ^ { 8 } } \right) ^ { 7 }$ and $d u / d x = \frac { 8 } { x ^ { 9 } }$

Question

Quizplus · Accepted Answer

The correct substitution for $u$ is $8 + \frac{1}{x^8}$, and differentiating this with respect to $x$ gives $d u / d x = - \frac{8}{x^9}$, matching option C.

Identify U And du/dxd u / d xdu/dx For the Integral ∫(8+1x8)8(−8x9)dx\int \left( 8 + \frac { 1 } { x ^ { 8 } } \right) ^ { 8 } \left( - \frac { 8 } { x ^ { 9 } } \right) d x∫(8+x81​)8(−x98​)dx

Identify U And $d u / d x$ For the Integral $\int \left( 8 + \frac { 1 } { x ^ { 8 } } \right) ^ { 8 } \left( - \frac { 8 } { x ^ { 9 } } \right) d x$