integration by substitution help

• Jul 15th 2009, 05:26 PM
mothra
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?
• Jul 15th 2009, 05:32 PM
Krizalid
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.
• Jul 16th 2009, 03:54 AM
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...
• Jul 16th 2009, 04:02 AM
mr fantastic
Quote:

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.
• Jul 16th 2009, 02:39 PM
mothra
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
• Jul 16th 2009, 03:27 PM
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.
• Jul 16th 2009, 05:11 PM
mothra
Quote:

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)