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amyna

  • one year ago

find the intergal:

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  1. amyna
    • one year ago
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    |dw:1441078962329:dw|

  2. freckles
    • one year ago
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    let u=ln(x)

  3. freckles
    • one year ago
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    \[\int\limits \tan(\ln(x) ) \cdot \frac{1}{x} dx \\ \text{ notice: the derivative of } \ln(x) \text{ w.r.t. } x \text{ is } \frac{1}{x} \]

  4. amyna
    • one year ago
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    ok then do i write tan as sin/cos?

  5. freckles
    • one year ago
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    yes

  6. freckles
    • one year ago
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    you write tan(u) as sin(u)/cos(u)

  7. freckles
    • one year ago
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    you can use another sub v=cos(u) so dv=-sin(u) du

  8. amyna
    • one year ago
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    |dw:1441079278529:dw|

  9. freckles
    • one year ago
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    why is dx/x still there

  10. amyna
    • one year ago
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    oh ya i mean du

  11. amyna
    • one year ago
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    so is the answer sin(1/x) / cos (1/x) ??

  12. amyna
    • one year ago
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    +c

  13. freckles
    • one year ago
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    \[\int\limits \frac{\sin(u)}{\cos(u)}du = \int\limits \frac{-dv}{v}=-\ln|v|+C \\ \text{ where } v=\cos(u)\]

  14. freckles
    • one year ago
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    and then replace u

  15. amyna
    • one year ago
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    ok got it thanks!

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spraguer (Moderator)
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is replying to Can someone tell me what button the professor is hitting...

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