How to integrate using u-sub? help please?

u = x-1

du = dx

int u^2/sqrt(u) du + int 2u/sqrt(u) du + int 1/sqrt(u) du

= int u^3/2 du + 2int sqrt(u) du + int (sqrt(u))^-1 du

= 2u^5/2 / 5 + 4u^3/2 / 3 + int u^-1/2 du

= 2(u^5/2) / 5 + 4(u^3/2) / 3 + 2(u^1/2) + C (I took exponentiated u's into parantheses to avoid confusion)

= (substitute back) 2((x-1)^5/2)/5 + 4((x-1)^3/2)/3 + 2((x-1)^1/2) + C is your answer.

Try u=x-1, du=dx. Then you have (u+1)^2/sqrt(u) du. Multiply out to get (u^2 + 2u + 1)/sqrt(u) du. Now you can separate this out to three easy integrals.

try u =x-1. Then du = dx and x = u+1. So your integral becomes:

integral ((u+1)^2 / sqrt(u) ) du

= integral (u^2 + 2u+1) / sqrt(u) ) du

= integral (u^(3/2) + 2u^(1/2)+u^(-1/2) ) du

which is a polynomial that integrates easily.

(don't forget to do the reverse conversion to x again when you're done integrating this).

Visit this website and press "show steps"

http://www.wolframalpha.com/input/?i=integrate+%28...