What is the Integral of #tan^5(x) dx#?

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Answer 1 · 2016-06-30T03:40:04

#int tan^5 x dx=1/4tan^4 x -1/2*tan^2 x+ln sec x+C#

The given is to find #int tan^5 x dx#

Solution:

#int tan^5 x* dx#

#int tan^5 x* dx=int tan^3 x*tan^2 x dx#

#int tan^5 x *dx=int tan^3 x*(sec^2 x-1) dx=int (tan^3 x sec^2 x-tan^3 x) dx#

#int tan^5 x* dx=int (tan^3 x sec^2 x)dx-int tan^3 x dx#

#int tan^5 x* dx=int (tan^3 x sec^2 x)dx-int tan^2 x *tan x dx#

#int tan^5 x* dx=int (tan^3 x sec^2 x)dx-int (sec^2 x-1) *tan x dx#

#int tan^5 x *dx=#
#int (tan^3 x sec^2 x)dx-int (tan x*sec^2 x)dx+int (tan x) dx#

#int tan^5 x *dx=1/4tan^4 x -1/2*tan^2 x+ln sec x+C#

God bless....I hope the explanation is useful.