Integration by Parts 5x ln(4x)dx

  • Thread starter sashab
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  • #1
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Homework Statement



Use integration by parts to evaluate the integral.
∫5x ln(4x)dx


Homework Equations



∫udv = uv - ∫vdu

The Attempt at a Solution


So here's my solution:
tumblr_n1a0635Kjb1tsd2vco1_500.jpg


But the computer is telling me I'm wrong :( We haven't learned how to integrate lnx yet, so the only choice I have is to make u = ln(4x) (even our textbook does this). Any help would be really appreciated! Thanks :)
 

Answers and Replies

  • #2
SammyS
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Homework Statement



Use integration by parts to evaluate the integral.
∫5x ln(4x)dx


Homework Equations



∫udv = uv - ∫vdu

The Attempt at a Solution


So here's my solution:
tumblr_n1a0635Kjb1tsd2vco1_500.jpg


But the computer is telling me I'm wrong :( We haven't learned how to integrate lnx yet, so the only choice I have is to make u = ln(4x) (even our textbook does this). Any help would be really appreciated! Thanks :)
What is the derivative of ln(4x) ?
 
  • #3
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What is the derivative of ln(4x) ?
Oh whoops! I can't believe I didn't notice such an obvious mistake. Thanks, I got the right answer now. :)
 
  • #4
HallsofIvy
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By the chain rule, the derivative of ln(4x) is (1/4x) times the derivative of 4x so (1/4x)(4)= 1/x.

Even simpler: ln(4x)= ln(x)+ ln(4) so its derivative is 1/x.
 

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