. trig substitution. use a trig substitution to evaluate the indefinite integral. show all the details of your substitution. dx/(x^2 sqrt(x^2 1))

The indefinite integral of dx / (x^2 √(x^2 + 1)) can be evaluated using trigonometric substitution. The result is arctan(x) + C.

To evaluate the indefinite integral ∫ dx / (x^2 √(x^2 + 1)), we can use the trigonometric substitution method.

Let's make the substitution x = tan(θ). This implies dx = sec^2(θ) dθ.

Substituting these values into the integral, we have:

∫ dx / (x^2 √(x^2 + 1)) = ∫ (sec^2(θ) dθ) / (tan^2(θ) √(tan^2(θ) + 1))

Now, we need to express tan^2(θ) and √(tan^2(θ) + 1) in terms of sec(θ).

Using the identity tan^2(θ) + 1 = sec^2(θ), we can rewrite the integral as:

∫ (sec^2(θ) dθ) / (sec^2(θ) √(sec^2(θ)))

Simplifying, we get:

∫ (sec^2(θ) dθ) / (sec(θ))

Canceling out the sec(θ) terms, we are left with:

∫ dθ

The integral of dθ is simply θ + C, where C is the constant of integration.

Finally, substituting back θ = arctan(x), the solution to the integral is:

∫ dx / (x^2 √(x^2 + 1)) = arctan(x) + C

Therefore, the indefinite integral of dx / (x^2 √(x^2 + 1)) is arctan(x) + C, where C is the constant of integration.

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The term for sounds that are not pleasing to our ears is "desonant."
O True
O False
Please help this is a TIMED test!! Thank u!

What is pictured below?

Should music lyrics be rated similar to the way movies are rated? One paragraph​

"Spoon ingredient into measuring cup until it is overfilled. Use a straight-edge spatula or the back of a knife to level off any
excess."
Liquid Measuring
B
Dry Measuring

Students who use text language in an online academic environment violate which rule of netiquette?

A)keeping content appropriate
B)practicing ethical behaviors

Which of the following career paths requires a college or university degree?
A costume designer
B master carpenter
C electrician
D grip

⚠️⚠️Please help me with 27 and 28

how are plants maintained

Types of element of art

NAME ALL 32 TEAMS IN THE NFL. NAME THE HEAD COACH, ONE OFFENSIVE PLAYER, AND ONE DEFENSIVE PLAYER EXAMPLE: LOS ANGELES RAMS. SEAN MCVAY, JARED GOFF, AARON DONALD

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What type of note gets 4 beats of sound?

What are the seven elements of design?

a. Color, Shape, Form, Line, Value, Texture, and Tone
b. Shape, Color, Form, Intensity, Line, Texture, and Space
c. Line, Shape, Value, Form, Color, Texture, and Space

What is the purpose of third person in epic theatre

What is an example of complimentary colors?

a. red-violet, blue-green, orange
b. orange, green, violet
c. orange and blue
d. green and yellow-green

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Which artist cut his ear off?​

Read this excerpt from Through the Looking-Glass by Lewis Carroll.

“You're wrong THERE, at any rate,” said the Queen: “were YOU ever punished?”

“Only for faults,” said Alice.

“And you were all the better for it, I know!” the Queen said triumphantly.

“Yes, but then I HAD done the things I was punished for,” said Alice: “that makes all the difference.”

Based on the details of this excerpt, the reader can infer that

Alice thinks it is fair to be punished for misbehavior.
Alice is punished quite often.
Alice has never been punished for anything.
Alice does not believe it is fair to punish children.

True or False: You measure 1/4 cup dry by filling a 1 cup dry measuring cup 1/4 of the way full.

Xavier is paraphrasing this passage from Through the Looking-Glass to help him understand what he reads.

“Are you a child or a teetotum?” the Sheep said, as she took up another pair of needles. “You'll make me giddy soon, if you go on turning round like that.” She was now working with fourteen pairs at once, and Alice couldn't help looking at her in great astonishment.

“How CAN she knit with so many?” the puzzled child thought to herself. “She gets more and more like a porcupine every minute!”

“Can you row?” the Sheep asked, handing her a pair of knitting-needles as she spoke.

“Yes, a little—but not on land—and not with needles—” Alice was beginning to say, when suddenly the needles turned into oars in her hands, and she found they were in a little boat, gliding along between banks: so there was nothing for it but to do her best.

Which detail would be important for Xavier to include in his paraphrase as he monitors his reading?

“Are you a child or a teetotum?”
“The needles turned into oars in her hands, and she found they were in a little boat.”
“She gets more and more like a porcupine every minute!”
“You’ll make me giddy soon.” HURRRY IM TIMMMMED

HELP ME PLZ!!!!!!!!!!!!!!!!!!

Look at the two types of syllogisms in Lesson 7. Give an original example of each type. Explain why each example is valid or invalid.

la importancia de los valores de
la ciudadanía y como joven que recomienda para ponerlos en práctica.


the importance of the values ​​of
citizenship and as a young person who recommends to put them into practice.

In the later Middle Ages, musicians and singers gradually began to add harmonies to chants. What did this action MOST likely mean
for music at that time?
O
Monophonic music was played more often.
Polyphonic music became more popular.
Organum music suddenly lost its popularity.
O
Lyrical poetry made a strong comeback.

Look at this image. These paintings were found in:

Which usually gives the feeling or finality to a piece
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How do you use evidence from the text to support your response to
Douglass’s personal narrative?

Research and write a paragraph of at least 5 complete and informative sentences about Eric Whitacre

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A slur looks like

Oan asterisk under the staff.
Oa dot over a note.
O the letters tr above a note.
O a curved line connecting two or more notes on the staff.​