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Recall that \[sec\ x = \frac{1}{cos\ x}\]
So you can just cancel 2 of the cosines.

Yes but they're to different powers.

Yes but
\[x^8 * \frac{1}{x^2} = x^6\]

You cannot. But \[cos^8x \ne cos(x^8)\]

\[cos^8x = (cos\ x)^8\]

oh i see, so after cancel how would I integrate cos^6(x)?

It quickly becomes a mess.

But it's doable.

Was it \(cos(x^3)sin(x)\) or was it \((cos^3x)sin(x)\)

i believe it was the first one. which can't be u-subbed, so I had no idea what to do.

Right, but the other one can be u-subbed.

So have to be sure you know which they're talking about.