Calculus Question?

Question

Evaluate:
-infiniti
∫ x dx/(x^2+5)^2
0

Answer 1

For this problem you would have to use partial derivatives:
d uv = u dv + v du so u dv = d uv - v du --»
∫ u dv = uv - ∫ vdu
Let u = x
du = 1
v = -1 / 2x (x² + 5)
dv = 1 / (x² + 5)²
..... (continued)
∫ u dv = uv - ∫ v du = -1 / 2(x² + 5) - ∫ -1 / 2x (x² + 5)²
= [- 1/ 2(x² + 5)]∞→0 - [2 / (x² + 5)³]∞→0
= 0.1 - 0.016 = 0.084

Hope it helps.


XR

Answer 2

Let u = x^2 + 5
Then du/dx = 2x -- > du/2 = xdx
So we have ∫ .5du/u^2 = ∫ .5 u^-2 du
You should be able to take it from here