Question

evaluate the indefinite integral of (x+3)/(x^2+6x+10)dx?

Answer 1

We have :
\[\int\frac{x+3}{x^2+6x+10}\mathrm dx=\frac12\int\frac{2x+6}{x^2+6x+10}\mathrm dx\\=\frac12\int\frac{(x^2+6x+10)'}{x^2+6x+10}\\=\frac{1}{2}\ln(|x^2+6x+10|)+c\\=\frac{1}{2}\ln(x^2+6x+10)+c\]

Answer 2

oh ya i got it..thanks