# How to integrate ∫ (x^2−9)^(3/2) dx?

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#int (x^2-9)^(3/2)dx#

I have used substitution x=3 sec u and can go up to

81 ∫ （sec u)^5 -2 （sec u)^3 +sec u) du.

I then try to use t=tan(u/2) to solve ∫ （sec u)^5 du but end up in a mess.

Please help.

I have used substitution x=3 sec u and can go up to

81 ∫ （sec u)^5 -2 （sec u)^3 +sec u) du.

I then try to use t=tan(u/2) to solve ∫ （sec u)^5 du but end up in a mess.

Please help.

##### 2 Answers

Apr 2, 2018

Solved!

#### Explanation:

use reduction formula or integration by parts to integrate (sec u)^5

Apr 3, 2018

I have solved this way.