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I've gotten pretty far I think,
set x= 1/3 sec(U)

then I got to the point where I had
\[81 \int\limits_{}^{} (\cos(x))^4 dx\]

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|dw:1327038086064:dw|

It seems like if you have made a mistake when substituting back for x.

I did this
|dw:1327038548902:dw|

I know I've done it correctly right up until the substitution

oops that last term should be over 8

There should be a term in the form \(ku\) in your integral, k is a constant.

is the integral |dw:1327039058333:dw|

I think that's where my missing term might be

Yeah.

And this is the term where the arctan came from, because \(u=\tan^{-1}{\sqrt{9x^2-1}}\).

Exactly.

Yeah, thanks a lot for your help!

You're welcome.

If you guys are still online I ran into problems with how this was working out.

I somehow need u= -arctan(1/sqrt(9x^2âˆ’1))

Why would you need that?

|dw:1327040345712:dw|

that is what it's telling me I'm missing from the end

|dw:1327040463342:dw|

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