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Having trouble with the antiderivative of this function

  • Thread starter jlt90
  • Start date
  • #1
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Homework Statement


Evaluate the indefinite integral:
[tex]\int[/tex]7x+1/x^2+1 dx


Homework Equations





The Attempt at a Solution


My first attempt at the solution was to try using substitution. I set u=x^2+1. so du=2x dx and x=sqrt(u-1). Then I rewrote the integral so it is [tex]\int[/tex]7du/4usqrt(u-1). This is where I don't know where to go with this attempt.

I'm pretty sure I'm going about this problem all wrong. If I could just get a push in the right direction I'd really appreciate it :)
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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Split the integral into 7x/(x^2+1) and 1/(x^2+1). The first one is the u-substitution you spoke of. The second is a trig substitution.
 
  • #3
4
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Thank you very much. So the first one becomes [tex]\int[/tex]7/2u du then 7/2ln(x^2+1) after taking the anti derivative and substituting x^2+1 for u. Then the second part becomes arctan x. So would the final answer be (7/2)ln(x^2+1)+arctan(x)?
 
  • #4
Dick
Science Advisor
Homework Helper
26,258
618
That looks fine to me.
 

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