Problem

Integrate each function by using the table in App…

Problem 34 Easy Difficulty

Integrate each function by using the table in Appendix $D$.
$$\int \frac{d x}{x-4 x^{2}}$$

Answer

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Calculus 1 / AB

Basic Technical Mathematics with Calculus

Chapter 28

Methods of Integration

Section 11

Integration by Use of Tables

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Video Transcript

So here on this problem we need to evolve it an indefinite integral which is integration dx over x minus four X square. And to evaluate this integral we have to refer the appendix D. That is given in the book. Now let me first rewrite this integration as integration and dx over now. I can take X. Comin from the denominator like this and here we'll get we'll get one minus four X. Now we can use one formula that is given in the appendix T. Of the book. And the formula is integration do you over you times A plus B. U. And it is equal to negative one over a natural log A plus B. You divide by you. Now if you compare uh the formula with the given integral and we can see that in our case you we have ex it is one and B s minus four. Now you can use exactly this formula to evaluate and struggle so negative one over A. So they were one natural log A plus B. U. So is one, B is minus four and us exhale divide by X, which can be written as negative. Natural lock one minus four X divide Biggs. So this is a required answer for the given problem. I hope you have understood the problem. Thank you.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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