What is the integral for tanx?
Find the integral for tanx.
Use tanx=sinxcosx.
∫tanxdx=∫sinxcosxdx
Let cosx=u. So, -sinxdx=du
∫tanxdx=-∫duu⇒∫tanxdx=-lnu+CCisaconstant.⇒∫tanxdx=-lncosx+C⇒∫tanxdx=lncosx-1+C⇒∫tanxdx=lnsecx+C
Hence, the integral of tanxis lnsecx+C where C is a constant.