Determine the indefinite integral
of negative sec squared six 𝑥 evaluated with respect to 𝑥.
To answer this question, it’s
almost simply enough to quote the general result for the integral of sec squared of
𝑎𝑥. It’s one over 𝑎 times the tan of
𝑎𝑥. It is sensible, though, to take a
factor of negative one outside of the integral as shown. And when we do, we obtain the
solution to be negative one times a sixth of tan six 𝑥 plus 𝑐. And all that’s left is to
distribute the parentheses. Negative one times a sixth of tan
six 𝑥 is negative one-sixth tan of six 𝑥. And negative one times 𝑐 gives us
this new constant, capital 𝐶. And so we find our indefinite
integral to be negative one sixth of tan of six 𝑥 plus 𝐶.