jackiemofo said:
Evaluate the trigonometric integral of:
\(\displaystyle \int\left[(secx)(tanx - secx)\right]dx\)
\(\displaystyle \int sec(x)tan(x)dx-\int sec^{2}(x)dx\)
First part: \(\displaystyle \int sec(x)tan(x)dx\)
Let \(\displaystyle u=sec(x), \;\ du=sec(x)tan(x)dx\)
\(\displaystyle \int du=u\)
resub:
\(\displaystyle =\boxed{sec(x)}\)
Second part:
\(\displaystyle sec^{2}(x)dx\)
Let \(\displaystyle u=tan(x), \;\ du=sec^{2}(x)dx\)
\(\displaystyle \int du=u\)
\(\displaystyle =\boxed{tan(x)}\)
So, put it together and we have:
\(\displaystyle \boxed{sec(x)-tan(x)}\)
\(\displaystyle \int (tan^{2}(y)+1)dy\)
Use the identity \(\displaystyle tan^{2}(y)=sec^{2}(y)-1\)
Then, you can use the result from the first part.
