How Do You Integrate ∫√((x^4)/2 + 9) dx?

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Homework Help Overview

The discussion revolves around the integration of the function ∫√((x^4)/2 + 9) dx. Participants are exploring methods to approach this integral, particularly focusing on the use of trigonometric substitution and its applicability given the function's structure.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Some participants suggest using trigonometric substitution as a potential method, while others express uncertainty about how to manipulate the function to fit this approach. There is also a discussion about the implications of the original poster's mistake regarding the power of x in the integral.

Discussion Status

The conversation is ongoing, with participants providing hints and suggestions. There is a recognition that the problem may require different approaches depending on the correct formulation of the integral. Some participants question whether trigonometric substitution remains valid for the corrected function.

Contextual Notes

Participants note that integration problems should be categorized appropriately within the forum, and there is a mention of the need for special functions if trigonometric substitution is deemed ineffective for the given integral.

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Homework Statement



∫√(((x)^2)/2 + 9) dx

Homework Equations



---

The Attempt at a Solution


I'm having a horrible time trying to do it. Problem is, I don't know how to start. The only thing I can think of is using trigonometric substitution. But I don't know how to manipulate the function in order to make it fit. A hint would be greatly appreciated.

*Edit* I made a mistake, it's
∫√(((x)^4)/2 + 9) dx I accidentally put it to the 2nd power instead to the 4th...
 
Last edited:
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MusicDragon said:

Homework Statement



∫√(((x)^2)/2 + 9) dx


Homework Equations



---

The Attempt at a Solution


I'm having a horrible time trying to do it. Problem is, I don't know how to start. The only thing I can think of is using trigonometric substitution. But I don't know how to manipulate the function in order to make it fit. A hint would be greatly appreciated.
Trig substitution is the way to go.

Note that x2/2 = (x/√2)2.
Draw a right triangle with vertical leg labeled x/√2 and horizonatal leg labeled 3. Work out a relationship between the angle θ and x.

BTW, integration problems should not be posted in the Precalc section. I am moving this thread to the Calculus & Beyond section.
 
Mark44 said:
Trig substitution is the way to go.

Note that x2/2 = (x/√2)2.
Draw a right triangle with vertical leg labeled x/√2 and horizonatal leg labeled 3. Work out a relationship between the angle θ and x.

I made a mistake on the equation to be integrated. It's to the power of 4, not 2. Does it still apply?
 
x4/2 = (x2/√2)2

Same advice as before, except label one leg (the opposite would be my choice) as x2/√2 instead of x/√2.
 
If it's sqrt(x^4/2+9) trig substitutions won't get you anywhere. You'd need special functions to do it.
 
Dick said:
If it's sqrt(x^4/2+9) trig substitutions won't get you anywhere. You'd need special functions to do it.

Absolutely.
 

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