Question

Integration of cubic root of tanx

Answer 1

∫tan^1/3 x dx    Take tanx = z ; sec²x dx = dz i.e dx = dz/(1+z²)

Putting t = 0, in the above, 

B+D = 0 ............ (1)

Putting t = 1, 

A + 2C + D = 1 ........... (2)

Putting t = -1,A + 2C-D = 1 ............ (3)

Using (2) & (3), D = 0

Therefore, B = 0 using (1)

A + 2C = 1 ................. (4)