Evaluating a simple integral

Question

I'm trying to evaluate a simple integral with basic rules we learned : $$\int\frac{2t+3}{9t^2-12t+8}dt$$ However I try, I fail. I tried substitution, splitting into two integrals and also square completion so I have this : $$\int\frac{2t+3}{9(t-\frac{2}{3})^2+4}dt$$ But it still leads me nowhere. What am I doing wrong?

Answer 1

Hint. You can split the given integral into $$ \int\frac{2t+3}{9t^2-12t+8}dt=a\int\frac{(9t^2-12t+8)'}{9t^2-12t+8}dt+b\int\frac{1}{9(t-\frac{2}{3})^2+4}dt. $$ Can you finish it?

Answer 2

Symbolab may help you

" https://www.symbolab.com/solver/step-by-step/%5Cint%20%5Cfrac%7B2t%2B3%7D%7B9t%5E%7B2%7D-12t%2B8%7Ddt "

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