Integration by parts MIDTERM really quick question please help

  • Thread starter banfill_89
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integration by parts!!!! MIDTERM...really quick question....please help!!!!

Homework Statement



[tex]\int[/tex] arctan4t dt


Homework Equations





The Attempt at a Solution



ive been attempting this all day. the answer is t arctan4t-1/8 ln(1+16t^2)+C

i get this asnwer up until the 1/8.......

a few steps befor emy answer i have t arctan4t - [tex]\int[/tex] 4t/ 1+16t^2

i dont kno whow to go from here to the answer....someone please help!!!
 

Answers and Replies

  • #2
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In your last integral, there's a fairly obvious substitution.

BTW, you need more parentheses: the integrand can be written more understandably as 4t/(1 + 16t^2)
 
  • #3
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what would be the substituition? in the book after thsi they factor out a 1/8......im lost
 
  • #4
Dick
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Substitute u=1+16t^2.
 
  • #5
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??? so am i integrating by parts again?
 
  • #6
Dick
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??? so am i integrating by parts again?
No, it's a u substitution.
 
  • #7
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i finnaly got it. this textbook sucks at explaining this. thanks guys. sorry dick i was confused at first cause u said let u= 16x^2+1 and i already used u. i get what you were saying now and it makes alot of sense. thanks!
 

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