integrate 1/((x)^(1/2)+9))
books answer is 2x^(1/2)-log((x)^(1/2)+9) + c
my question is can you also integrate this as 1/((x)^(1/4)^(2))+3^(2) to get (1/3) inverse tan x/3 + c????
are these different versions of the same answer???
No you cannot use inverse tan here... the power at the bottom is 1/2, NOT 2.
You have
Make the substitution . This will lead you to a quotient of two linear equations; simplify them using polynomial division, and then the result should be easy to integrate.