Having trouble with the antiderivative of this function

[jlt90]

Homework Statement

Evaluate the indefinite integral:
\int7x+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 \int7du/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 :)

 

[Dick]

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.

 

[jlt90]

Thank you very much. So the first one becomes \int7/2u 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)?

 

[Dick]

That looks fine to me.