Video Transcript
Determine the integral of six times
the sec squared of five 𝑥 with respect to 𝑥.
In this question, we’re asked to
evaluate the integral of a trigonometric function. And in this case, we can recall an
integral result which will help us evaluate this. We know for any real constants 𝑎
and 𝑘, where 𝑎 is not equal to zero, the integral of 𝑘 times the sec squared of
𝑎𝑥 with respect to 𝑥 is equal to 𝑘 times the tan of 𝑎𝑥 all divided by 𝑎 plus
the constant of integration 𝐶. And we can apply this directly to
the integral given to us in the question. We’ll set our value of 𝑘 equal to
six and our value of 𝑎 equal to five.
So by substituting these values
into our integral result, we get six times the tan of five 𝑥 divided by five plus
our constant of integration 𝐶. And we’ll rewrite this as six over
five times the tan of five 𝑥 plus 𝐶.
Therefore, we were able to show the
integral of six times the sec squared of five 𝑥 with respect to 𝑥 is equal to six
over five times the tan of five 𝑥 plus 𝐶.
