Hi this is one of question that i have got stumbling on.
This is just simple question using trigonometric substitution.
i do understand the solution process.
But What i wanna know is that it uses sin for finding solution but what if use cos instead?
my approach concluded into -arccos(x/4)+c which is say wrong answer but still if i differentiate it, it will be as same as original function in integral, which means it is also correct answer!
Guess i am missing some silly simple thing. Hope someone can help me out
Remember that when you integrate a function you get MANY antiderivatives. That's why there is a $+C$ in answers, and it could change things. Here is video about a similar problem made by Numberphile.