chapter 9

We obtain the following integral formulas by reversing the formulas for differentiation of trigonometric functionsthat we met earlier:

∫sin u du=−cos u+K
∫cos u du=sin u+K
∫sec2u du=tan u+K
∫csc2u du=−cot u+K

Integral of sec x, csc x

These are obtained by simply reversing the differentiation process.

∫sec u tan u du=sec u+K∫csc u cot u du=−csc u+K

Example 3: Integrate: ∫csc 2x cot 2x dx

Integral of tan x, cot x

Now, if we want to find ∫tanx dx, we note that
∫tanx dx=∫sinxcosxdx
Let u=cosx, then du=−sinx dx.                 done by:aishu
∫tanx dx=∫sinxcosxdx=−∫duu=−ln|u|+K=−ln|cosx|+