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.

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