Question

Evaluate: ${\int }_0^2(e^x+\frac{1}{2x+1})dx$

• A. $e^2-1$
• B. $e^2+\frac{ln5}{2}$
• C. $e^2-1+\frac{ln5}{2}$
• D. $e^2-\frac{ln5}{2}+1$

Answer 1

The correct option is C $e^2-1+\frac{ln5}{2}$

${\int }_0^2(e^x+\frac{1}{2x+1})dx=(e^x+\frac{ln(2x+1)}{2}){|}_0^2$
$=(e^2+\frac{ln5}{2})-(e^0+0)$
$=(e^2+\frac{ln5}{2})-1$