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silverangel's avatar

Another math question... help!

Asked by silverangel (939points) January 15th, 2012

The question is: use the substitution u^2=2x+5 to integrate ∫x√(2x+5) dx

I just need to know how to obtain du/dx, I don’t need the rest of the solution.. please HELP!!

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4 Answers

Mariah's avatar

if u^2 = 2x+5 then u = (2x+5)^(½). Then just use chain rule.

silverangel's avatar

well i tried that but i couldn’t reach the right part which is 2u(du/dx)=2, this is the stage i want to reach….

Mariah's avatar

Hmm, I’m not sure that that result it right. It looks like you tried to do an implicit derivative, but there’s an error.

Implicit differentiation is when you take the derivative of an an equation when it’s not in the form y = f(x). That is the case with your function up there. But when you do that for this function, you should get a slightly different answer than what you wrote. Furthermore, I’m not sure that implicit differentiation is the right way to go about a u substitution.

finkelitis's avatar

Either way should work. Silverangel, all you need to do is put (du/dx) on one side of your equation, and everything else on the other, then plug in for u like Mariah suggested in her first response.

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