SOLUTION: Integral of squareroot(x^2-4)^3 dx

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Question 1117235: Integral of squareroot(x^2-4)^3 dx
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=2sec%28u%29
x%5E2=4sec%5E2%28u%29
dx=2sec%28u%29tan%28u%29du
So,


sqrt%28%28x%5E2-4%29%5E3%29dx=%0D%0A2%282%5E3%2Atan%5E3%28u%29%29%2Asec%28u%29tan%28u%29du
sqrt%28%28x%5E2-4%29%5E3%29dx=%0D%0A16tan%5E4%28u%29%2Asec%28u%29du
sqrt%28%28x%5E2-4%29%5E3%29dx=%0D%0A16%28sec%5E2%28u%29-1%29%5E4%2Asec%28u%29du


You can now integrate by parts or use partial fractions.