Question

need help with this questionm, its improper integrals, and the question is integral from -infinity to infinity, xdx/(x^2+4)^3/2

Answer 1

try subbing out the x^2 + 4 and see what happens.

Answer 2

this is Calc 2 you know

Answer 3

not sure what calc 2 means.

this is a straight integral, but i thought a sub might make it easier if you do not see the direct approach.

the limits of integration cannot be the problem, AFAICS.

i will leave you to i unless there is something that you think i could add.

Answer 4

after making substitution
----> u = x^2 + 4
----> du = 2x dx
you have
\[\frac{1}{2} \int\limits_{-\infty}^{\infty} \frac{du}{u^{3/2}} = -\frac{1}{\sqrt{u}} = -\frac{1}{\sqrt{x^2 +4}}\]
Now apply limits, note that lim 1/infty = 0