? cos(x) dx = sin(x) + c
? sin(x) dx = -cos(x) + c

* * * *

Note that you can divide each term in the numerator by sec(x) to get:

? 4/sec(x) + tan(x)/sec(x) dx
==> ? 4cos(x) + sin(x)/cos(x) * cos(x) dx
==> ? 4cos(x) + sin(x) dx
==> ? 4cos(x) dx + ? sin(x) dx
==> 4 ? cos(x) dx + ? sin(x) dx

Therefore, by integration, we obtain:

4sin(x) - cos(x) + c

I hope this helps!

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