# Integrate (((x)^2)/2 + 9)

MusicDragon

## Homework Statement

∫√(((x)^2)/2 + 9) dx

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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...

Last edited:

Mentor

## Homework Statement

∫√(((x)^2)/2 + 9) dx

---

## 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?

Mentor
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.