Integrating the square root of a linear function.

[cptrsn]

Homework Statement

\int\sqrt{2*x-1}

Homework Equations

The Attempt at a Solution

Homework Statement

Obviously this can be fixed with the antiderivative of a linear function with proper constants i.e. \int A\times f(bx + c) = \frac{A}{b} F(bx + c), however my instructor provided me with a "clue" which I somehow can't seem to work out.

He claims that \int\sqrt{2*x-1} is equivilant to \int u^2 using "the right" substitution. My idea usually is:
1) u = \sqrt{2*x - 1}
2) x = u^2
3) dx = 2u du

Which would lead to \int u dx = \int u 2u du = \int 2u^2 du.
Obviously this is NOT identical to what he suggests, so can anyone point me in the right direction? I'm quite keen to know how he see such a problem.

 

[rootX]

If u = sqrt(2x-1)
then how x = u^2?

 

[Bohrok]

I don't think he quite knew what he was talking about; there are some problems with that which I wouldn't even try to work with or fix.
What part of the integrand can u be that will easily let you integrate with respect to u?

 

[HallsofIvy]

The teacher not being here to defend himself, I might suggest that cptrsn did not quite remember what the teacher had suggested. Any time you have a linear term, ax+ b, an obvious substitution is just u= ax+ b so that du= adx.