1. integration by substitution help

Ok, so i have a problem from my book that I can't figure out how to start,

so the integral is from 0 to 4 (not important) and it is (x/(1+2x)^1/2 ) dx

i can't see any value in the equation for "u" that will remove x from the equation. Could someone please explain what you would select for "u" and why? Do you have to modify the integrand before proceeding?

2. That root is annoying so let's get rid of it by putting $u=\sqrt{1+2x}$ (get the new bounds for $u$ according this substitution!), which can be rewritten backwards as $u^2=1+2x.$ Now differentiate and make the substitutions.

3. i dont understand, if i differentiate 1 + 2x then i no longer have an x term and I cant remove the x in the numerator...

i must be missing something...

4. Originally Posted by mothra
i dont understand, if i differentiate 1 + 2x then i no longer have an x term and I cant remove the x in the numerator...

i must be missing something...
You've been given the substitution to use. Have you been taught how to integrate by making a substitution? If so, please post all your working and say where you get stuck.

5. yes, ive been taught to integrate by substitution, but can you not see how this problem is atypical and confusing? I have not been taught to substitute anything other than "u" and i dont see how subing u^2 as 1+2x will help me, other than by removing the root, can someone maybe go through the problem step by step with explanations, sorry im just lost

6. As per Krizalid's suggestion, the substitution $u^{2}=1+2x$

means that $x=\frac{u^{2}-1}{2}, \;\ dx=udu$

See?. Can you make the subs now?. Don't forget to change the limits of integration. That is a common oversight.

7. Originally Posted by galactus
As per Krizalid's suggestion, the substitution $u^{2}=1+2x$

means that $x=\frac{u^{2}-1}{2}, \;\ dx=udu$

See?. Can you make the subs now?. Don't forget to change the limits of integration. That is a common oversight.
Thank you, I guess I have never made multiple substitutions in the same equation so I wasn't thinking in those terms. I verified my answer by using integration by parts on the same problem and it checked out. I was just required to solve the problem using substitution for some reason (because james stewart is an ass)