YES! Because the antiderivative of IS . There are no two ways about it.
must tan be part of the solution, I haven't learned that yet and it is hard for me to grasp! Will I not get the solution if I do not use arctan or take a trigonometric approach. I have only gone as far as intgrating sin and cos back and forth.
where does the r come from? for u^r?
To differentiate with respect to x, you would have to use the chain rule. Its derivative is not just but that times the derivative of : .
That is why, to integrate you would make the substitution so that and not only replace in the integral with u but replace with
"Substitution" in integration is the reverse of the "chain rule" in differentiation. But, unlike differentiation, instead of "adding something", you are "taking away something" and that "something" already has to be there! You can move constants in and out of the integral but not functions of the variable.
You could, for example, integrate by writing it as and using the substitution but you cannot do that with because there is no "x" in the numerator and you cannot put one there.
You really need to know that to do this problem. I suggest you talk to your teacher about why this problem was given if you have not yet studied the derivative of arctangent.