Mathematics: Evaluate the integral. (use c for the constant of integration.) 7 ln(x)/ x sqrt(5 + (ln(x))^2) dx

Evaluate the integral. (use c for the constant of

Ответ:

01030901

15.03.2022

Okay, so we have

$\int\limits { \dfrac{7ln(x)}{x \sqrt{5+ln(x)^2}}} \, dx$ .

Substitute u=ln(x)^2+5

and differentiate.
$dx= \dfrac{x}{2ln(x)}du$
$\dfrac{7}{2} \int\limits { \dfrac{1}{ \sqrt{u}}} \, du$

$\int\limits { \dfrac{1}{ \sqrt{u}}} \, du = 2 \sqrt{u}$

$\dfrac{7}{2} \int\limits { \dfrac{1}{ \sqrt{u}} } \, du = 7 \sqrt{ln(x)^2+5}+C$

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Ответ:

Adones5104

21.11.2022

Mathematics

Step-by-step explanation:

A. d = r/t

r = dt

B. distance = rate/time

800,000/4 = 200000

r = dt

200,000(4) = 800,000

C. 800/4 = 200

This is because kilo means 1000

D. It is easier to use kilometers because when using bigger numbers it is easier to simplify into smaller numbers with bigger units.

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Evaluate the integral. (use c for the constant of integration.) 7 ln(x)/ x sqrt(5 + (ln(x))^2) dx

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