Trigonometric substitution of (x^2+8x)

[playoff]

Homework Statement

Hello PF, I am taking calculus II right now, and a homework problem I came to ponder upon has been giving me big trouble today. Here is the what I have to take the integral of:

∫x/(x^(2)+8x)^(1/2) dx

Every other trig substitution problems were straight forward, as all I had to do was identify what trig identity I could use. But this time, I have no idea where to start from.

Homework Equations

The Attempt at a Solution

In wishful thinking I set substitution for x=(8^(1/2))tan(t), but as expected it didn't work out after.

Help would be greatly appreciated!

 

[Simon Bridge]

$$\int \frac{x}{\sqrt{x^2+8x}}\;dx$$... you need a substitution that makes the term inside the radical a complete square.

That is the point behind trig substitutions.
So try completing the square inside the radical first.

 

[playoff]

$$\int \frac{x}{\sqrt{x^2+8x}}\;dx$$... you need a substitution that makes the term inside the radical a complete square.

That is the point behind trig substitutions.
So try completing the square inside the radical first.

OK, I didn't know how to complete a square until now. I tried, and I'm making progress now, thank you!

 

[Simon Bridge]

You looked it up - well done :)
Let me know how you get on.

 

[verty]

Sorry, what I had here was not correct. I think the best thing is to remove it.