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What is the indefinate integral

  • Thread starter sora4ever1
  • Start date
:confused: :confused: i have this question can any one help me plz thx.


what is the indefinate integral of tan^7xsec^4x goodluck.
 

Answers and Replies

TD
Homework Helper
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What have you tried so far?
 
TD said:
What have you tried so far?
:redface:
i am not yet to that grade lvl yet so that is why i want some one to post this explaing how to do it and little back ground to this thx :biggrin:
:surprised
 
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Basically, I believe you must simply save a factor of [tex] \sec ^ 2 x[/tex]

and use [tex]\sec ^ 2 x = 1 + \tan ^ 2 x [/tex] to express the remaining factors

in terms of [itex] \tan x [/itex]. Next, simply substitute with respect to [tex] \tan x [/tex].

(I think it's called "u"-substitution in some texts).?


As you should already know, :shy:
[tex] \frac{d}{dx} \tan x = \sec ^ 2 x [/tex]

*Here's that method, put in action :smile: :
[tex] \int {\tan ^7 x\sec ^4 x\,dx} = \int {\tan ^7 x\left( {1 + \tan ^2 x} \right)\sec ^2 x\,dx} = [/tex]
[tex] \int {\tan ^7 x\left( {1 + \tan ^2 x} \right)\,d\left( {\tan x} \right)} = \boxed{\frac{{\tan ^8 x}}{8} + \frac{{\tan ^{10} x}}{{10}} + C} [/tex]

!It is very likely that somewhere I made an error!....:frown: :frown: :frown:
Somewhere...some silly error :rolleyes:
 
Last edited:
bomba923 said:
Basically, I believe you must simply save a factor of [tex] \sec ^ 2 x[/tex]

and use [tex]\sec ^ 2 x = 1 + \tan ^ 2 x [/tex] to express the remaining factors

in terms of [itex] \tan x [/itex]. Next, simply substitute with respect to [tex] \tan x [/tex].

(I think it's called "u"-substitution in some texts).?


As you should already know, :shy:
[tex] \frac{d}{dx} \tan x = \sec ^ 2 x [/tex]

*Here's that method, put in action :smile: :
[tex] \int {\tan ^7 x\sec ^4 x\,dx} = \int {\tan ^7 x\left( {1 + \tan ^2 x} \right)\sec ^2 x\,dx} = [/tex]
[tex] \int {\tan ^7 x\left( {1 + \tan ^2 x} \right)\,d\left( {\tan x} \right)} = \boxed{\frac{{\tan ^8 x}}{8} + \frac{{\tan ^{10} x}}{{10}} + C} [/tex]

!It is very likely that somewhere I made an error!....:frown: :frown: :frown:
Somewhere...some silly error :rolleyes:
thx a lot.
 
TD
Homework Helper
1,020
0
bomba923 said:
!It is very likely that somewhere I made an error!....:frown: :frown: :frown:
Somewhere...some silly error :rolleyes:
No, this is correct :smile:
 

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