Derivatives and integrals?

Question

I was given this problem to solve for but I just can't figure it out:
∫(dsqrt(1+x^4)dx )/dx

Answer 1

Oh this one is easy! Remember the following

If ∫f(x)dx = g(x)

then g'(x)=f(x)

The derivative is the opposite function of the integral you see?

So in your problem you are taking the derivative then the integral, so you should get the function you started with back (plus C if you want to be technical)

So your answer is:

sqrt(1+x^4) + C


ADDITIONAL:

So in formula terms...

∫f'(x)dx = f(x)+C

Answer 2

Since integration and differentiation are inverse operations by the Fundamental Theorem of Calculus, the answer is just sqrt(1 + x^4) + C given that the question reads:
integral of the derivative of sqrt(1 + x^4). Now you could painfully go through both operations but noting this fact is much simpler.

Answer 3

∫(dsqrt(1+x^4))/dx
=sqrt(1+x^4)+C