The problem is

(x^4) / (sqrt x^10 -2)

I thought I could use U- Substitution first and work it out like that...but that doesn't pan out. Help please this one has me stumped. (Speechless)

Printable View

- Jun 14th 2008, 01:57 PMJonathanEyoonIntegrating using Trig Substitution
The problem is

(x^4) / (sqrt x^10 -2)

I thought I could use U- Substitution first and work it out like that...but that doesn't pan out. Help please this one has me stumped. (Speechless) - Jun 14th 2008, 02:05 PMMathstud28
Let $\displaystyle x^5=\varphi$

so $\displaystyle d\varphi=5x^4dx$

Giving us

$\displaystyle \frac{-1}{5}\int\frac{d\varphi}{2-\varphi^2}$

Now let $\displaystyle \varphi=\sqrt{2}\tanh(\theta)$

and go from there

EDIT:

I am sorry I misread it, it should be

$\displaystyle \frac{1}{5}\int\frac{d\varphi}{\sqrt{\varphi^2-2}}$

Now let $\displaystyle \varphi=\sqrt{2}\sec(\theta)$ - Jun 14th 2008, 02:33 PMJonathanEyoon
- Jun 14th 2008, 02:35 PMMathstud28
- Jun 14th 2008, 03:01 PMJonathanEyoon
Ok made the correction for tanTheta and ended up with having to integrate secTheta which my final line is

(1/5) ln l sectheta + tantheta l + C

Now looking at my teachers answer, this is far from correct but i'm not sure as to how to proceed from here. - Jun 14th 2008, 03:06 PMMathstud28
- Jun 14th 2008, 03:16 PMJonathanEyoon
MmMm.... how are you getting those values? I remember the teacher saying something about drawing a triangle to figure out how to get everything back in terms of x. I think this is the part but I didn't understand it too well. Could you show me?

- Jun 14th 2008, 03:42 PMMathstud28