Question

The integral of 1/(x^2+9)^(3/2)dx
Ive been trying to solve this for 2 hours please help!

Answer 1

\[\int\limits \frac{ 1 }{ \sqrt{(x^2+9)^3} }dx\]

Answer 2

Thats the problem Im doing...But its to the power of (3/2)

Answer 3

hey,
i couldn't figure out the substitution by inspection so i looked up the step by step on wolfram alpha, it's a tan substitution...

Answer 4

rewrite \[\sqrt{(x^2+9)^3}\] as \[\left(\sqrt{x^2+9}\right)^3\]

trigonometric substitution \[x=3\tan \theta\] follows

Answer 5

\[(a)^\frac{ 3 }{ 2 } = \sqrt[2]{a^3}\] @sirm3d has the right idea. Use trig subsitution.

Answer 6

Please check answer

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Answer 9

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Answer 13

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