Question

kindly help me with this
evaluate the integral
$\gamma \binom{2}{1} \frac{2x}{{x}^{2} + 1} dx$
​

Answer 1

Answer:  ln5 - ln2 ≈ 0.919

Step-by-step explanation:

$\int\limits^2_1 {\dfrac{2x}{x^2+1}} \, dx\qquad \qquad =\int\limits^2_1 {(x^2+1)^{-1}} \, 2xdx$

Let u = x² + 1    →    du = 2x

$\text{Then we have:}\quad \int\limits^2_1 {u^{-1}} \, du \qquad =ln|u|\bigg|^2_1$

Substitute u = x² + 1

$ln|x^2+1|\bigg|^2_1\quad =ln|2^2+1|-ln|1^2+1|\quad = ln|5|-ln|2|$