Question

Complete the table to find the indefinite integral. (Use C for the constant of integration.)

Answer 1

Step-by-step explanation:

Note the expression below can be rewritten as

$\dfrac{1}{(2x)^3} = \dfrac{1}{8x^3} = \dfrac{1}{8}x^{-3}$

Therefore, the we can rewrite the integral as

$\displaystyle \int \dfrac{dx}{(2x)^3} = \frac{1}{8}\int x^{-3}dx$

$\;\;\;\;\;\;\;\;\;\;= \dfrac{1}{8}\left(\dfrac{x^{-2}}{-2}\right) + C$

$\;\;\;\;\;\;\;\;\;\;= -\dfrac{1}{16x^2} + C$