



 
Hi Meghan, Write 4x^{2}  25 as 4(x^{2}  25/4) and then [ 4x^{2}  25]^{3/2} = 4^{3/2} [ x^{2}  25/4]^{3/2 }= 8 [ x^{2}  25/4]^{3/2} = 8 [ x^{2}  (5/2)^{2}]^{3/2}. Now I can see that the substitution is x = 5/2 sec(θ). With this substitution the denominator becomes
The substitution also yields dx = 5/2 sec(θ) tan(θ) dθ. Perform the substitution, convert the secant and tangent functions to sines and cosines and see if you can evaluate the resulting integral. Good luck in this,  


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