Difficulty to find this integral

DDarthVader

1. The problem statement, all variables and given/known data
Hi! I'm not being able to solve this integral: [tex]\int \sqrt{2ax}\; dx[/tex] We have started with integral yesterday and I don't know much yet.



2. Relevant equations



3. The attempt at a solution
This is what I tried to solve the integral
[tex]\int \sqrt{2ax}\; dx = \int u^{\frac{1}{2}}\; du = \frac{2}{3}{}u^{\frac{3}{2}}=\frac{2}{3}\sqrt[3]{(2ax)^2}[/tex]

sharks

Assuming that a is a real constant,
[tex]\int \sqrt{2ax}\; dx = \int \sqrt{2a}\sqrt x\; dx= \sqrt{2a} \int \sqrt x\; dx[/tex]
Since [itex]\sqrt x[/itex] is the same as [itex]x^{\frac{1}{2}}[/itex], you can easily find its integral, and then multiply by [itex]\sqrt {2a}[/itex] to get the final answer.

Mark44

When you use a substitution, as you obviously did above, you need to write down what the substitution is. IOW, you should have u = <...> somewhere close by.

Also, u^3/2 = ##\sqrt{u^3}##, not ##\sqrt[3]{u^2}##, which is what you had.