Mathematics: Kindly help me with this evaluate the integral

Kindly help me with this evaluate the integral

mrashrafkotkaat

30.01.2022

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

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

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200002977

27.09.2020

1/2 ( 6e - 3f - 3/4)

Multiply 1/2 by the numbers in parentheses.

3e - 3/2f - 1/8

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