Question

what change of variables would be used for the integral $int(16 - 8x)^{-3}dx$?
choose the correct answer below.
a. $u = 8x$
b. $u=(16 - 8x)^{-2}$
c. $u = 16 - 8x$
d. $u = 3x$

Explanation:

Step1: Recall substitution rule

In substitution for $\int f(g(x))g'(x)dx$, we set $u = g(x)$. Here $f(u)=u^{-3}$ and $g(x)=16 - 8x$.

Step2: Determine substitution

To simplify $\int(16 - 8x)^{-3}dx$, we set $u = 16 - 8x$ as it is the inner - function in the composite function $(16 - 8x)^{-3}$.

Answer:

C. $u = 16 - 8x$