Trig Substitution (?) Integral

[rty640]

Homework Statement

The answer is:

The Attempt at a Solution

I tried trig substitution, letting x =$$\sqrt{2}$$tan($$\theta$$) and using the identity 1+tan$$^{2}$$=sec$$^{2}$$($$\theta$$), but couldn't get to the answer.

Thanks for the help.

 

[Mark44]

Show us what you did, and we can set you straight. That looks like the right substitution.

 

[rty640]

http://i48.tinypic.com/10dh6jl.jpg

 

[Mark44]

Now undo your first substitution, which was x = sqrt(2)tan(theta). It will be helpful to draw a right triangle (I didn't see one in your work). The acute angle is theta. The opp. side is x, the adj. side is sqrt(2), and the hypotenuse is sqrt(x^2 + 2). Convert your secant terms back to terms involving x, and see if that gets you to your answer.

Your work looks pretty good - I didn't see anything obviously wrong, but I just scanned it quickly, so might have missed something. When you get your final answer, check it by differentiating it - you should get 11x^3/sqrt(x^2 + 2).

 

[rty640]

I'm not sure if what I have simplifies to the answer.

http://i45.tinypic.com/28tckqq.jpg

 

[vela]

You forgot to cube the root 2 in the denominator of the second term in the square brackets.

You're also off by a sign. You flipped the sign when you went from tan to sec when integrating.

 

[rty640]

I got it now, thanks a lot.