Question
Thu September 24, 2009 By:

  where f(x) = (sec4x) dx /

Sir can you answer the following question?

Expert Reply
Fri September 25, 2009

Substitute y = tan x

dy/dx = sec2 x

dy = sec2 x dx

f(x) = (sec2 x sec2 x)/tan x

= (1 + tan2 x)(sec2 x)/tan x

Hence f(x) dx = (1 + tan2 x)(sec2 x)dx/tan x

f(x) dx = (1 + y2)dy/y1/2 = f(y)dy

(y-1/2 + y2-1/2)dy = (y-1/2 + y3/2)dy

= 2y1/2 + 2y5/2/5

= 2tan x (5 + tan2 x)/5

Regards,

Team,

TopperLearning.

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