# Trig Substitution (?) Integral

## Homework Statement  ## 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.

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Mark44
Mentor
Show us what you did, and we can set you straight. That looks like the right substitution.

Mark44
Mentor
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).

vela
Staff Emeritus