$\displaystyle\int_2^3 \dfrac{x\,dx}{x^2+1}$ equals

Question

Accepted Answer

A. $\dfrac{1}{2}\log 2$

1. Put $t=x^2+1$, $dt=2x\,dx$, so $x\,dx=	frac12 dt$.
2. Antiderivative: $\dfrac{1}{2}\log(x^2+1)$.
3. Evaluate: $\dfrac{1}{2}[\log 10-\log 5]=\dfrac{1}{2}\log\dfrac{10}{5}=\dfrac{1}{2}\log 2$.
4. Option B drops the $	frac12$ factor.
_Source: syllabus Mathematics Ch 7 "Integrals", p.337_

Answer

$\log 2$

Answer

$\dfrac{1}{2}\log\dfrac{5}{2}$

Answer

$\dfrac{1}{2}\log\dfrac{3}{2}$

$\displaystyle\int_2^3 \dfrac{x\,dx}{x^2+1}$ equals

Keep practising Straight Lines and Conic Sections