Integration Question: integrate x(x + 3)^0.5

[johnboy]

One of my homework problems on integrating is x(x+3)^.5.

I solved it and got (2/5)u^(5/2)-2(u)^3/2+C

This answer though does not match my book's answer.

Is my answer correct, but I just didn't simplify it to a single fraction? Thank you..

 

[pka]

The correct answer is:
\(\displaystyle \frac{2}{5}\left( {x + 3} \right)^{\frac{5}{2}} - 2\left( {x + 3} \right)^{\frac{3}{2}} + C.\)

 

[johnboy]

whoops, sorry i left that i u form. but that is why i had, thank you.

 

[johnboy]

Quick question (sorry), when i derive that, im not getting x(x+3)^.5... well, maybe i am but its in another form. how can u derive it to make it in the form x(x+3)^.5? Thanks!

 

[stapel]

[W]hen derive that, [I'm] not getting x(x+3)^[0].5.

Please reply showing your steps and what you are getting when you differentiate the result provided earlier. (The tutors will be glad to help you find your error, if any, but they need to be able to see your work in order to do that.)

Thank you.

Eliz.

 

[johnboy]

...(x+3)^(3/2)-3(x+3)^(1/2)

 

[stapel]

I'm going to guess that your post represents the first step in your differentiation.

...(x+3)^(3/2)-3(x+3)^(1/2)

But what did you do next, to simplify? You factored out the sqrt[x + 3], and... then what?

Please show all of your steps, and describe what you are doing, as necessary. Thank you.

Eliz.

 

[pka]

\(\displaystyle \L
\left( {x + 3} \right)^{\frac{3}{2}} - 3\left( {x + 3} \right)^{\frac{1}{2}} = \left( {x + 3} \right)^{\frac{1}{2}} \left( {\left( {x + 3} \right) - 3} \right) = x\sqrt {x + 3}\)