Evaluate : ∫tanx/(secx + tanx)dx ii. ∫cosecx/(cosecx - cotx)dx

Question

Evaluate :

i. \(\int\frac{tanx}{(secx\,+\,tanx)}dx\) 

∫tanx/(secx + tanx)dx

ii. \(\int\frac{cosecx}{(cosecx\,-\,cotx)}dx\)

∫cosecx/(cosecx - cotx)dx

Answer 1

i. Given:

Multiply and divide by (secx - tanx)

= sec x-tan x + x + c

ii. Given:

Multiply and divide by (cosec + cotx)

= -cot x-csc x + c