Video Transcript
Determine the indefinite integral
of negative sec squared six 𝑥 with respect to 𝑥.
To answer this question, it’s
almost simply enough to quote the general result for the integral of sec squared
𝑎𝑥, where in our case the constant 𝑎 is equal to six. The result tells us that the
integral of sec squared 𝑎𝑥 with respect to 𝑥 is one over 𝑎 times the tan of 𝑎𝑥
plus constant 𝑐. It’s sensible, however, before
using this result to take the factor of negative one outside the integral as
shown. So when we do perform our
integration, we obtain the solution to be negative one times one-sixth of tan of six
𝑥 plus 𝑐, recalling that in our case the constant 𝑎 is equal to six.
And now all that’s left is to
distribute the parentheses. Negative one times one-sixth of tan
six 𝑥 is negative one-sixth tan of six 𝑥. And negative one times the constant
𝑐 gives us this new constant uppercase 𝐶. And so we find our indefinite
integral to be negative one-sixth of tan of six 𝑥 plus 𝐶.
