Integration question

[MrJoe2000]

I'm looking to solve a simple integral but I can't seem to get started.

Int[(ax)^1/2]dx

Can someone show me how to do this?

 

[pka]

I'm looking to solve a simple integral but I can't seem to get started.
Int[(ax)^1/2]dx
Can someone show me how to do this?

What is the derivative of \(\displaystyle \tfrac{2}{3}\sqrt{a}x^{\frac{3}{2}}~?\)

 

[MrJoe2000]

That's the answer I got but the book says (2x(ax)^1/2)/3 + C. Where are they getting that other "x" term from outside the root?

 

[mmm4444bot]

Both expressions are the same.

x*sqrt(x) = x^(2/2)*x^(1/2) = x^(3/2)

 

[pka]

That's the answer I got but the book says (2x(ax)^1/2)/3 + C. Where are they getting that other "x" term from outside the root?

\(\displaystyle \tfrac{2}{3}\sqrt{a}x^{\tfrac{2}{3}}=\tfrac{2}{3}x\sqrt{ax}.\)

\(\displaystyle \sqrt {x^3 } = x\sqrt x \)

 

[MrJoe2000]

Now I just feel stupid. Thanks for the clarification!