Help!!!!! Evaluate the indefinite integral
20tan^6x

Question

Help!!!!! Evaluate the indefinite integral 
20tan^6x

hartnn · Answer

1) split up tan^6 as tan^4 . tan^2
2)write tan^2 = 1+sec^2
3) put t= tan x

hartnn · Answer

sorry, tan^2 = sec^2-1

hartnn · Answer

and 3) t= tan x only in the integral having sec^2x

anonymous · Answer

so $$20\int\limits_{}^{}\tan ^{4}x(\sec ^{2}x-1)$$

hartnn · Answer

do same thing for tan^4x dx

hartnn · Answer

yes, go on

anonymous · Answer

now i split tan^4x again?

hartnn · Answer

first do t^4(s^2-1) = t^4s^2 - t^4

so in 1st integral, t^4s^2 put tan x =t 

and split up t^4 as t^2.t^2

hartnn · Answer

separate the 2 integrals...
did u understand that ? or confused because i wrote t and s for tan and sec ?

anonymous · Answer

no i get that

anonymous · Answer

so 
t^4s^2-t^2*t^2

hartnn · Answer

solve the 2 integrals separately...else you will get confused, because the 2nd integral is again going to split up into 2

anonymous · Answer

alright i see that. but where do i go from here. u substitution of the first part?

hartnn · Answer

yes

anonymous · Answer

so
$$4\tan ^{5}-(20\int\limits_{}^{}\tan ^{4}x)$$

hartnn · Answer

yeah, solve t^4 in same manner.

anonymous · Answer

so 
$$\tan ^{5}x-\frac{ 20 }{ 3 }\tan ^{3}x+20tanx-20x$$

anonymous · Answer

+ C of course

hartnn · Answer

be careful with the signs..

anonymous · Answer

Those should be the correct signs according to the answers section in my book.  Thanks for your help I was really struggling with this question

hartnn · Answer

oh, okk :) 
i though +20/3 will come, but anyways,
welcome ^_^