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Integrate each of the given functions.$$\int \frac{6 d z}{z^{2} \sqrt{z^{2}+9}}$$

$-\frac{\sqrt{z^{2}+9}}{3 z}+C$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 8

Integration by Trigonometric Substitution

Integrals

Campbell University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

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in the problem we have been given integration six dessert upon the square and the route They're required plus nine. So for this we will put jail equals three dan theater. And this it becomes today six quarter to de Tita. So it becomes six integration 36 squad tita de tita Bond 9 10 squad theater and the route nine dan squad tita plus nine Further it is witness six integration today sake tita into seek to to the theater. Born nine dan squatty to and two three Zeke tita. Hence these T three and these three councils each other 60- 62 cancels each other. Therefore this integration becomes six integration sick tita de tita upon 9 10 Squad Tita. So it is equal to two abound 3 indication cost squared tita. D Theta upon cost tita into science choir tita because we have converted sick and can't dance for tita into science custom. So therefore we have this cost data and this power cancels each other. Therefore we have two upon 3 integration casita de tita upon sign squad tita. Now for this solution for solving this integration will assume sign theta equals T. Therefore it it becomes cause theater the theater equals D. D. Now this is Regina has to upon three division DT upon the square. That equals to two upon three. Integration T. To the power minus two DT. That equals to upon three T. To the power minus one upon minus one plus C. Or further. This is equal to minus two upon three into one upon scientific to plus C. Now this can be written us -2 in the root over off. Get a square plus nine upon three. Did plus see So this is integration of six digit upon route. Uh Get square the route over. Aww your a squared plus nine. So this equals two minus two root overall. Very squared plus nine divided by treated plus C. So this is the answer to the problem.

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