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Integrate each of the given functions.$$\int \frac{6 p^{3} d p}{\sqrt{9+p^{2}}}$$

$2\left(9+p^{2}\right) \sqrt{9+p^{2}}-54 \sqrt{9+p^{2}}+C$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 8

Integration by Trigonometric Substitution

Integrals

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in the problem we have been given integration 19th six P G D P Upon Uvarov nine Plus Pay Square. Now for solving this problem will assume big was 3 10 theater dip equal 36 square theater data. To no This is written as six. Integration 27. Thank you to to into three into six Squad Theatre. The theatre upon Fruit over of nine into 1 plus dan squad tita. Now this is equal to six integration 81 Tan Que Tita In the six sq Tita de Tita upon three 60 to This is equal to 1 62. Integration Don Quixote to sick tita. The tita now further shelving this equal stoop 162 into integration Dennis square theater in Bhutan tita sake theater to the theater. Now late safety deposit key odd 60 to Dante to Did you take was duty Further we have this equals two 1 62 into integration six quarter to -1 into tan theta sick tita lita. This is equal to 162 into integration Do you Square -1 Ditty that is equal to 162 into Due to the Power three upon 3 -D. Now this is equal to 162 into Sick. You teed up on three minus seek tita Further we have this equals two 162 upon three into one plus piece choir upon this is Squire, So peace quite upon nine To the power of 3.2 -162 into one plus He is quite upon 9 to the power of half Further this equals two This is 54 Rather this is 54 should be written like this so it is 54 Into nine plus piece choir upon nine To the power one and 2 nine Plus piece choir to the Upon 9 to the power half this becomes this that minus this is 54 into route over off one plus P esquire plus C. This is equal to twice Into nine plus piece choir in the root over of nine plus P square minus 54. Underwrote one plus PS choir plus C. So we have this as two into 9 plus B sq into whatever off nine Plus piece choir -64 Under Road one Plus piece choir plus see so this is the answer to the problem.

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