document.write( "Question 1117235: Integral of squareroot(x^2-4)^3 dx \n" ); document.write( "

Algebra.Com's Answer #732306 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"x=2sec%28u%29\"$
\n" ); document.write( " $\"x%5E2=4sec%5E2%28u%29\"$
\n" ); document.write( " $\"dx=2sec%28u%29tan%28u%29du\"$
\n" ); document.write( "So,
\n" ); document.write( "

\n" ); document.write( "

\n" ); document.write( " $\"sqrt%28%28x%5E2-4%29%5E3%29dx=%0D%0A2%282%5E3%2Atan%5E3%28u%29%29%2Asec%28u%29tan%28u%29du\"$
\n" ); document.write( " $\"sqrt%28%28x%5E2-4%29%5E3%29dx=%0D%0A16tan%5E4%28u%29%2Asec%28u%29du\"$
\n" ); document.write( " $\"sqrt%28%28x%5E2-4%29%5E3%29dx=%0D%0A16%28sec%5E2%28u%29-1%29%5E4%2Asec%28u%29du\"$
\n" ); document.write( "

\n" ); document.write( "

\n" ); document.write( "You can now integrate by parts or use partial fractions.
\n" ); document.write( " \n" ); document.write( "

\n" );