For the math whizzes!!!!?

Question

What is the antiderivative of x((x^2)+3)^1/2?

Answer 1

Using substiutions:

v = x^2 + 3
dv = 2x dx or dv / 2 = x dx

We can now substitute back into the equation and integrate:

Integral (v^1/2)/2 dv

which using the power rule and simplifying

v^(3/2)/3 + C - substitute back in for v leaves [(x^2 + 3)^(3/2)]/3 + C

Answer 2

(1/3)(x² + 3)^(3/2) + C

Now *you* get busy and figure out why. (HINT: it's a composite function ☺)


Doug