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anonymous

  • one year ago

evaluate the integral integral of (ln(4x))^2dx

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  1. anonymous
    • one year ago
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    im assuming this is integration by parts. but i am not sure what to make my u and what to make dv

  2. anonymous
    • one year ago
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    would ln(4x) be good for u? and i would use chain rule to find derivative?

  3. Astrophysics
    • one year ago
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    \[\int\limits (\ln(4x))^2 dx\] is it like this?

  4. anonymous
    • one year ago
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    yes it is

  5. Astrophysics
    • one year ago
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    You can just let u = (ln(4x))^2 and dv = 1

  6. anonymous
    • one year ago
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    hey astrophysics can you please help me I posted a question

  7. anonymous
    • one year ago
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    ok! where do you get the 1 from?

  8. anonymous
    • one year ago
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    pls help i need to get rest

  9. Astrophysics
    • one year ago
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    We can think of there being a 1 when we have such functions dv=dx, it's like if you have to integrate tanx dx you would use by parts, lets u = tanx, and dv = dx

  10. Astrophysics
    • one year ago
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    I guess it would've been better if I said dv = 1*dx

  11. anonymous
    • one year ago
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    ohh yes i see! thank you

  12. anonymous
    • one year ago
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    astro pls help

  13. Astrophysics
    • one year ago
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    Not tanx I meant arctanx haha

  14. anonymous
    • one year ago
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    hmm im not getting the right answer.. is it correct to say that the integral of ln4 is = to xln4 ?

  15. anonymous
    • one year ago
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    \[(\ln(4x))^{2}x-\int\limits x \frac{ 2\ln4 }{ x } dx\]

  16. anonymous
    • one year ago
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    so then i cancel out the x on the outside and the x in the denominator..

  17. anonymous
    • one year ago
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    and i am left with the integral of 2ln4, so then i take out the 2 and put it behind the integral, and i am left with the integral of ln4

  18. anonymous
    • one year ago
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    from there i took the integral of ln4 which i believe is xln4 and i put both parts together but the answer is incorrect

  19. anonymous
    • one year ago
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    \[(\ln(4x))^2x-2xln4\] that is my answer..

  20. anonymous
    • one year ago
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    but the answer says incorrect..

  21. imqwerty
    • one year ago
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    the answer is \[x(\ln (4x))^2-2xln (4x)+2x\] recheck once again :)

  22. Jhannybean
    • one year ago
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    You're almost there.

  23. anonymous
    • one year ago
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    thank you.. i am not seeing where the 2x at the end comes from.. ?

  24. anonymous
    • one year ago
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  25. anonymous
    • one year ago
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    that is my work so far

  26. imqwerty
    • one year ago
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    u=4x \[\int\limits\frac{ (\ln (u)) }{ 4}du \]after some vry bad calculations nd simplifications u get- \[\frac{ 1 }{ 4 }((u)(\ln (u))^2 -2\ln (u)+2(u))\]and then when u simplify nd put u=4x then u get that answer..

  27. anonymous
    • one year ago
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    ok i see, thank you!

  28. imqwerty
    • one year ago
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    no prblm but that is a long method..

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