cosecant? Well, their time has come.
Example 10: Find ∫tan x dx.
First, rewrite this integral as
Now, we let u = cos x and du = − sin x dx and substitute.
∫ −
Now, integrate and re-substitute.
∫ − = ln|u| = ln|cos x| + C
Thus, ∫ tan x dx = − ln |cos x| + C.
Example 11: Find ∫ cot x dx
Just as before, rewrite this integral in terms of sine and cosine.
Now we let u = sin x and du = cos x dx and substitute.
∫^
Now, integrate.
ln |u| + C = ln |sin x| + C