Evaluate the Integral

[lovetolearn]

Is this the correct answer?


Evaluate the following integrals


1
∫ ((2x)/(sqrt1+2x))dx
0


ITG = (2/3)*(x-1)*sqrt(2x+1) + C

ITG(1) = 0
ITG(0) = -2/3
ITG(1) - ITG(0) = 2/3
--> 2/3

[HallsofIvy]

No, it isn't. Unfortunately, since you did not show how you did the integral, I cannot say how to correct it. Did you make the sustitution u= 1+ 2x?

[lovetolearn]

I attached a picture of my work below. Thank you for looking over this problem. Where did I go wrong?

[HallsofIvy]

When you make the substitution [tex]u= v^2[/tex], you have dv= 2udu but you have treated it as if it were du= 2vdv.

Instead, use the fact that [tex]\frac{u-1}{\sqrt{u}}= u^{1/2}- u^{-1/2}[/tex].