What is the antiderivative of this?

Question

What is the antiderivative of x/((16+x^2)^(1/2))?
(x / the square root of (16 + x^2))?

What method did you use? Substitution, etc..?

Thanks!

Answer 1

Let 16 + x^2 = u
2x dx = du
Your integral becomes the integral of
(1/2) u^-1/2 du
which is
u^1/2 = sqrt(16 + x^2)

Answer 2

Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)
f(x) = (x + 3)(5x − 1)