Question

Evaluate: $\int \frac{2x+1}{x^2+x}dx$

• A. $\log x+\log (x+1)$
• B. $\frac{3}{2}\log x$
• C. $\frac{1}{2}\log (x+1)$
• D. None of these

Answer 1

The correct option is A $\log x+\log (x+1)$

Let $\frac{2x+1}{x^2+x}=\frac{2x+1}{x(x+1)}=\frac{x+x+1}{x(x+1)}=\frac{1}{x}+\frac{1}{1+x}$
$\int \frac{2x+x}{x^2+x}dx$
$=\int \frac{1}{x}+\frac{1}{1+x}dx$
$=\log x+\log (x+1)$