Integration problem

  • #1
How does one integrate
[tex]\int\arctan 4t\,dt[/tex]
?

This is out of a section on integration by parts. Maybe that would help but I don't see any "parts." I only see one, the arctan.
 

Answers and Replies

  • #2
Math Is Hard
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Let u = arctan4t
dv = dt
 
  • #3
Thank you so much. Please tell me if I did this correctly.
Integration by Parts:
[tex]\int u\,dv = uv - \int v\,du [/tex]

[itex]u = \arctan 4t , \,dv = dt , v = t\,dt , \,du = \frac{4}{16t^2 + 1}[/itex]
[tex]\int\arctan 4t\,dt = t\arctan 4t - \int\frac{4t}{16t^2 + 1}\,dt = t\arctan 4t - \frac{1}{8}\ln(16t^2 + 1) + C [/tex]
 
  • #4
Math Is Hard
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yup! looks good to me!
 

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