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Difficult integral

  • Thread starter alba_ei
  • Start date
  • #1
38
1

Homework Statement


[tex] \int \frac{\sin x+\cos x}{\sec x+ \tan x}dx [/tex]

Homework Equations



[tex] \sin x = \frac{1}{\sec x} [/tex]
[tex] \cos x = \frac{\sin x}{\tan x} [/tex]


The Attempt at a Solution


i separate and try to use identities but i got nothign

1/(secx^2+secx tan x)+sin x/tanx^2+sec x :confused:
 
Last edited:

Answers and Replies

  • #2
mjsd
Homework Helper
726
3
write everything in terms of sin x and cos x only, then integrate with change of variable.
 
  • #3
cristo
Staff Emeritus
Science Advisor
8,107
73
One of your identities is incorrect: sec(x)=1/cos(x).

As has been said above, you should first look to express everything in terms of sines and cosines. See if this gives you a hint as to how to proceed.
 
  • #4
5
0
please tell more

this is the shape that i got
don't know how to complete

–integral sin²x-sin2x-1/2(1+sinx)
 
  • #5
Gib Z
Homework Helper
3,346
5
[tex]-(\int \sin^2 x dx - \int \sin 2x dx - 1/2\int 1+\sin x)[/tex]

Write sin^2 x as (1/2) (1-cos2x).

for sin 2x, make a substitution u=2x, then remember the integral of sin u is -cos u.

For the 3rd one, if you can't do it, why are you doing this question?
 
  • #6
44
0
you can also try weierstrass substitution
i.e t = tan x/2
 

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