To make a good substitution, it is important to get rid of original letters like x or t in the function because we cannot integrate the function if there are two letters in the function.

Also, if there is a square root in the function, it is better to let u equals to a letter in the square root because it would be easier to integrate.

Finally, it is important to change the form by using trig identity. We learned that sin^2+cos^2=1 and tan^2+1=sec^2. Sometimes, it might be really helpful to change the form if sin^2, cos^2, tan^2, and sec^2 are in the function.