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

[MusicDragon]

Homework Statement

∫√(((x)^2)/2 + 9) dx

Homework Equations

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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...

 

[Mark44]

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.

 

[MusicDragon]

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?

 

[Mark44]

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.

 

[Dick]

If it's sqrt(x^4/2+9) trig substitutions won't get you anywhere. You'd need special functions to do it.

 

[Curious3141]

If it's sqrt(x^4/2+9) trig substitutions won't get you anywhere. You'd need special functions to do it.

Absolutely.