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Denebel

  • 4 years ago

Use the given trig identity to set up a u-substitution and then evaluate the indefinite integral.

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  1. Denebel
    • 4 years ago
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    |dw:1326790438109:dw|

  2. FoolForMath
    • 4 years ago
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    Yes, where are you stuck?

  3. imperialist
    • 4 years ago
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    Hint: what is the derivative of tan(x)?

  4. Denebel
    • 4 years ago
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    How to start? Can I do this ? |dw:1326790556349:dw|

  5. Denebel
    • 4 years ago
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    Derivative of tan x is (sec x)^2

  6. imperialist
    • 4 years ago
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    Yes, so try only breaking one of the (sec x)^2 into 1+(tan x)^2

  7. imperialist
    • 4 years ago
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    You will be pleasantly surprised!

  8. FoolForMath
    • 4 years ago
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    \[ \int \sec^4 x \space dx = \int (1+\tan^2 x) \sec^2 x \space dx \]

  9. FoolForMath
    • 4 years ago
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    Now put \( \tan x = z \implies \sec^2 x dx = dz \)

  10. FoolForMath
    • 4 years ago
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    So, \[ \int (1+\tan^2 x) \sec^2 x \space dx = \int (1+z^2) dz \] I am sure you can proceed after this.

  11. Denebel
    • 4 years ago
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    Oh I see now. Thank you very much!

  12. FoolForMath
    • 4 years ago
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    Glad to help :)

  13. imperialist
    • 4 years ago
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    Likewise :)

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