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Integral Help

  • #1

Homework Statement


solve the integral.


Homework Equations


integral (sec(x)^2 / 4+tan(x)^2)


The Attempt at a Solution


i tried replacing the numerator with the trig identity: tan(x)^2 + 1 -- but not sure what else to try.
 

Answers and Replies

  • #2
3,812
92
There is a very obvious substitution you can do here.
 
  • #3
Consider the derivatives of trigonometric functions.
 
  • #4
was the step i performed correct?
 
  • #5
SammyS
Staff Emeritus
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was the step i performed correct?
No.

What is the derivative of tan(x) ?
 
  • #6
What is d/dx (tanx)?
Edit: or what sammy says :)
 
  • #7
90
2
Also, be careful that an integral is not the same thing as an antiderivative.
 
  • #8
HallsofIvy
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The first thing I would do is replace sec2(x) with 1/cos2(x) and replace tan2(x) with sin2(x)/cos2(x).
 
  • #9
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The first thing I would do is replace sec2(x) with 1/cos2(x) and replace tan2(x) with sin2(x)/cos2(x).


I wouldn't do this, but I would take a look at tanx and what the derivative is, it does become pretty hard though and you need a trig substitution afterwards, I think I did this exact problem before.
 
  • #10
90
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