IDNLearn.com: Where your questions meet expert advice and community insights. Ask your questions and get detailed, reliable answers from our community of knowledgeable experts.

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


Complete The Table To Find The Indefinite Integral Use C For The Constant Of Integration class=

Sagot :

Step-by-step explanation:

Note the expression below can be rewritten as

[tex]\dfrac{1}{(2x)^3} = \dfrac{1}{8x^3} = \dfrac{1}{8}x^{-3}[/tex]

Therefore, the we can rewrite the integral as

[tex]\displaystyle \int \dfrac{dx}{(2x)^3} = \frac{1}{8}\int x^{-3}dx[/tex]

[tex]\;\;\;\;\;\;\;\;\;\;= \dfrac{1}{8}\left(\dfrac{x^{-2}}{-2}\right) + C[/tex]

[tex]\;\;\;\;\;\;\;\;\;\;= -\dfrac{1}{16x^2} + C[/tex]

The indefinite integral of [tex]\int \frac{1}{(2x)^{3} }\, dx[/tex] is [tex]- \frac{1}{16x^{2} }+c[/tex].

What is the indefinite integral of [tex]\frac{1}{(2x)^{3} }[/tex]?

Given:

  • [tex]\int \frac{1}{(2x)^{3} }\, dx[/tex]

Find:

  • The indefinite integral of the given expression.

Solution:

[tex]\frac{1}{(2x)^{3} }[/tex]

We can also write the above expression as:

[tex]\frac{1}{(2x)^{3} } = \frac{1}{8x^{3} } = \frac{1}{8} x^{-3}[/tex]

Now, we solve it for indefinite integral, and we get;

[tex]\int \frac{dx}{(2x)^{3} } = \frac{1}{8} \int x^{-3} dx[/tex]

Now, applying the integration formula, we get;

[tex]= \frac{1}{8}\frac{x^{-2} }{-2} +c[/tex]

[tex]=-\frac{1}{16x^{2} } +c[/tex]

Hence, the indefinite integral of the  [tex]\int \frac{1}{(2x)^{3} }\, dx[/tex] is [tex]- \frac{1}{16x^{2} }+c[/tex].

To learn more about indefinite integral, refer to:

https://brainly.com/question/12231722

#SPJ2