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Trig Substitution (?) Integral

  • Thread starter rty640
  • Start date
  • #1
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Homework Statement



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The answer is:

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The Attempt at a Solution




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

Thanks for the help.
 

Answers and Replies

  • #2
33,630
5,288
Show us what you did, and we can set you straight. That looks like the right substitution.
 
  • #4
33,630
5,288
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).
 
  • #6
vela
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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.
 
  • #7
16
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I got it now, thanks a lot.
 

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