Question

for the integral x((x^2+16)^(1/2)) I solved for the arcsin part, the x^2+16^1/2, but I don't know how I was supposed to break the two parts up. I tried integration by parts and it seems worse.

Answer 1

lets see i think its simpler than you are making it

just try a substitution:
u = x^2 +16
du = 2x dx ---> dx = du/2x

\[\rightarrow \frac{1}{2} \int\limits \frac{du}{\sqrt{u}}\]
see how the "x" on top is cancelled out because du has an "x"

Answer 2

Ok ya actually that totally works...which is weird because part a says perform the appropriate trig substitution on the integral and then part b says complete the calculation of the integral by evaluating the resulting trig integral from the previous part....but this seems much easier