SOLUTION: Find the integral ∫▒(x √(1-x^2)) dx

Rewrite as



Let 

Then 

Solve for dx.  

Substitute for u and du





Cancel the x's




The -2 on the bottom is the same as a multiplication by
 and can be brought out in front of the integral:



Next we use the formula 
with 



The  on the bottom is a division by  which is the
same as a multiplication by  which we can take out in front
of the integral sign.  So we have:



Finally we replace u using 



-----------------------

That's a long process, but later you will learn this shortcut:



Since the derivative of  is , and we
already have an x factor, we only need to put in 
and take out , since they would cancel:



Then you just observe that that is in the form 
without writing any u's or du's.

Then you add 1 to the exponent and multiply by the reciprocal
of the new exponent:


 


Edwin