Integration using Substitution - Need Help with Specific Question (1 Viewer)

[__moonriver]

Hi,

I'm lost. I feel like I'm missing some important information about integration using substitution which causes me to keep getting the wrong answer.

e.g. Use the substituion u = 2x - 5 to find (Integration sign) x(2x-5)[-1/2] dx

(the [-1/2] is meant to be an indice, sorry, it's hard to notate this on the computer)

This is what I did:

u = 2x-5
du = 2 dx

x = (u + 5)/2

(Integration sign) x(2x-5)[-1/2] dx
= 1/2 (Integration sign) 2x(2x-5)[-1/2] dx
= 1/2 (Integration sign) (u+5) . 2u[-1/2] du


Well I don't really know where to go from there.
Was I even on the right track?

 

[azureus88]

you can split the (u+5)/u^0.5 into u^0.5 + 5u^-0.5 and then integrate as usual.

 

[lolokay]

 

[tacogym27101990]