Trig Substitution

Question

∫(x^2)/((16-x^2)^(3/2))dx

 

I keep on getting the wrong answer. 

Answer 1

Let      r=theta

 

Use the substitution 

 

x = 4sinr                   x² = 16sin²r

dx = 4cosr dr

 

Then rewrite the integral using the substitution.  Now your integral to evaluate will be in terms of theta. Simply the integral using your trigonometric identities.  Once you have your final solution, substitute back into x.