anonymous
  • anonymous
Use the given trig identity to set up a u-substitution and then evaluate the indefinite integral.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
|dw:1326790438109:dw|
anonymous
  • anonymous
Yes, where are you stuck?
anonymous
  • anonymous
Hint: what is the derivative of tan(x)?

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anonymous
  • anonymous
How to start? Can I do this ? |dw:1326790556349:dw|
anonymous
  • anonymous
Derivative of tan x is (sec x)^2
anonymous
  • anonymous
Yes, so try only breaking one of the (sec x)^2 into 1+(tan x)^2
anonymous
  • anonymous
You will be pleasantly surprised!
anonymous
  • anonymous
\[ \int \sec^4 x \space dx = \int (1+\tan^2 x) \sec^2 x \space dx \]
anonymous
  • anonymous
Now put \( \tan x = z \implies \sec^2 x dx = dz \)
anonymous
  • anonymous
So, \[ \int (1+\tan^2 x) \sec^2 x \space dx = \int (1+z^2) dz \] I am sure you can proceed after this.
anonymous
  • anonymous
Oh I see now. Thank you very much!
anonymous
  • anonymous
Glad to help :)
anonymous
  • anonymous
Likewise :)

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