How can I integrate this equation? (to get surface area of the mobius strip)

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enter image description here I'm in the process of calculating surface area of the Mobius strip. I've derived the surface element so far and I got the equation above. Now, I need to integrate in terms of $s$ and in terms of $t$ (or I can integrate in terms of $t$ first and then $s$). However, I'm facing some difficulties that how can I transform or possibly substitute the equation in the form that can be integrated. Help me.