Answered

Discover new perspectives and gain insights with IDNLearn.com. Get timely and accurate answers to your questions from our dedicated community of experts who are here to help you.

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 :

Trancescientidn

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

We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. IDNLearn.com has the answers you need. Thank you for visiting, and we look forward to helping you again soon.