The integral of (t^.5)lntdt from 1 to 8!?

Question

I my answer of 78.221 is wrong....I tried to solve it using integration by parts...any help?? thanks!!!

Answer 1

let let v = t^.5

the limits now become from v = 1 to v = 8^.5

t = v^2

dt = 2v dv

Int [v * ln(v^2) * 2v] dv

log rules: ln(a^n) = n ln(a)

Int [v * 2ln(v) * 2v] dv

Int [4v^2 ln(v)] dv

now use parts

Int [u * dv] = uv - In [v * du]

let u = ln(v)

du = 1/v dv

let dv = 4v^2

v = (4/3)v^3

= (4/3)v^3 lnv - int [(4/3)v^3 * 1/v] dv

= (4/3)v^3 lnv - int [(4/3)v^2] dv

= (4/3)v^3 lnv - (4/9)v^3

evaluate and you should get 21.756075

Answer 2

integration by parts works fine ..u = ln t....{ [2/3] t^(3/2) ln t - [4/9] t^(3/2) }