Calculus question. There seems to be inconsistency and no explanation on u substitution.

Hi Michael,

These problems may look similar, but they are two very different problems. Just because they have a similar format does not mean they will be solved the same way.

The original problems are both different from each other, and in both solutions a different u value is chosen to solve the problem. This is what produces the different steps for each problem. 

In the first problem only part of the radicand is replaced by u, and the resulting expression happens to be the derivative of the arcsin function, which is why we get a trig function when we antidifferentiate.

In the second problem, u replaces all of the radicand, which allows us to antidifferentiate using the exponent rule, so no trig functions are necessary.