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Integrate each function by using the table in Appendix $D$.$$\int \frac{\sqrt{3+4 x^{2}} d x}{x}$$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 11

Integration by Use of Tables

Integrals

Missouri State University

Campbell University

Harvey Mudd College

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

02:46

Use substitution to find e…

00:54

02:32

Use tables to perform the …

01:08

01:58

Use a table of integrals t…

01:11

Evaluate each integral.

03:37

01:17

Find each integral.$$\…

01:39

01:53

Evaluate each definite int…

So here on this problem we need to evaluate an indefinite integral. Which is integration under Route three plus four X square divide by X. Dx. And to evaluate this entry level we have to refer the appendix D. That is given in the book. Now let me first rewrite this integration hours. Integration under route Now this three can be written us under three square plus four X square can be written us two X whole square like this. Not D X divided by X. Now we can refer one formula that is given in the appendix D. And the formula is integration under route a square plus you square divide by you dot do you? Is it cold too? Just underwrote you square plus a square minus a natural log. A plus underwrote you square plus a square divide by U plus C. So I'm going to use this formula to evaluate this integral. If you compare this formula with this in trouble if you can say that in our case we have U. Equals two two weeks. And do you? It is equal to two D. X. And the value of a. We have route three. We can do one thing. We can multiply the numerator and the denominator with two. So that we get the standard format. Now these two dx. We have do you and you we have two weeks now we can easily evaluate this integral by using exactly this formula. So it will be equals two. Now underwrote U squared plus a squared. You square. We have two X whole square. So it would be four X square plus. No this route three square would be three minus. This is route three. Natural log A. We have route three plus. Underwrote you square plus a square. So you square we have four X square plus a square. We have three divide by you. We have two weeks plus. See where this C. Is a concert of integration that will come because it's an indefinite intrude. So this is a required answer for the given integral, which was integration underwrote three plus four X square divide by X. Dx. So I hope you have understood the problem. Thank you.

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