It is mostly just memorized.
But, there is a cool way to go about it I am sure.
Let's integrate it then this way.
Rewrite as
Now, let
Now, make the subs and it is rather easy.
Resub:
Here is the original problem
(Sin(x))^2/ cos(x)
I used an identity and converted the numerator to 1 - (cos(x))^2
I broke apart the fraction and got
1 / cos(x) - cos(x)
I know how to integrate cos(x) but I haven't a clue as to how to integrate sec(x). Any help or hints is appreciated!
Thansk in advance
multiply the top and the bottom by so you'll have
Notice that is the derivative of which means that when you integrate the function, you'll get the log of that funcion...
which leads us to this solution:
from that, we can get these solutions, which sometimes are more helpful:
or
Well, you could, but I realise now you still have to integrate secx
Put u=tanx and dv/dx=sinx
then du/dx=sec^2x and v= -cosx
so the integral of sinx.tanx= -tanx.cosx + (integral of)secx
So yup, not much use if you don't know secx, hence the post I guess.
Ah damn, my first post as well!