integrate cube root of tan x end root

Asked by ashokanvinayakan | 6th Jan, 2020, 09:36: PM

Expert Answer:

integrate cube root of tan x end root

begin mathsize 16px style straight I equals integral cube root of tanx dx
Put space cube root of tanx equals straight t
straight t cubed equals tanx
straight x equals tan to the power of negative 1 end exponent straight t cubed
dx equals fraction numerator 3 straight t squared over denominator 1 plus straight t to the power of 6 end fraction end style
 
begin mathsize 16px style straight I equals integral fraction numerator straight t cross times 3 straight t squared over denominator 1 plus straight t to the power of 6 end fraction dt equals integral fraction numerator 3 straight t cubed over denominator 1 plus straight t to the power of 6 end fraction dt end style
Put t2 = y
2tdt = dy
 
Error converting from MathML to accessible text.
Use partial fraction method to solve further.

Answered by Sneha shidid | 7th Jan, 2020, 10:26: AM