Evaluate using Substitution

[kggirl]

Evaluate the inegral using substition for integral from 0 to 1 x/(x^2 - 5)^3 dx

This is what I have:

integral from 0 to 1 x/(x^2 - 5)^3 dx =

1/(1^2 -5)^3 = 1/(1-5)^3 = 1/(-4)^3 = 1/-64

Is this correct?

 

[Gene]

Substitute u = x²-5
du = 2xdx
dx=du/2x
x*dx/(x²-5)^3 =
(1/2)du/u^3 =
(1/2)u(-3)du integral from u=-5 to -4

 

[kggirl]

So after substituting, is the final answer .00125

 

[Gene]

One typo. Hope it didn't throw you
(1/2)u^(-3)du integral from u=-5 to -4 =
(1/2)(1/-2)u^-2 [-5 to -4] =
-.25(1/16-1/25) =
-.005625

Or you can unsub to get
-.25(x^2-5)^-2 [0 to 1]
= -.25(x^2-5)^-2 [0 to 1]
=-.25(1/(1-5)^2-(0-5)^2
= -.25(1/16-1/25)
---------------
Gene

 

[kggirl]

I'm not sure if i'm doing this right still:

1/2 integral from -4 to -5 U^3du =

1/2[U^3+1 du/4] from -4 to -5=

1/2 * 4 [u^4] from -4 to -5 =
2[-5^4 - (-4)^4] =
2[-625+256] =
2*369 = 738