The equation is the integral of (x^3)(sqrt(1+x^2). The steps say that u=(1/2)x^2, where do they get that from?

Use the product rule to find the derivative of (– 4æ° + 9x*)(6e" + 5) Use e^x for e". You do not need to expand out your answer.

use trig substitution to find integral of 1/[3t^2(6-t^2)^(1/2).   that is numerator is 1 denominator is 3 t-squared times the square root of 6-t-squared.   I tried letting t=square root of six times cosx. I worked it to the point where I have 1 over 18 times square root 6 times cos^2(x) sin(x).  then i brought those to numerator in the form of sec^2(x)csc(x) with 1 over 18 square root 6 going outside of the integral.  If I did this correct up to this point, how can I solve if it is in terms of sec and csc?  Thanks!

Integrate the indefinite integral sqrt(16-x2)/6x2